roulette 16 number board history
March 25th, 2019 at 11:00:12 PM
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I know of someone who believes the dealer manipulates the wheel and ball spin to produce duplicates. He says there is no way that a number can appear on the board 3 times, or two numbers on the board twice each (or certainly both) without the dealer manipulating the wheel and ball spin. I say this is bogus but I would like to have probabilities (if they aren't that low, which I suspect) to prove him wrong.
With a history of the last 16 numbers, what is the probability of:
a) one number appearing 3 times
b) two numbers each appearing twice
c) both a) and b), one number appears 3 times and two other numbers appear twice
thanks
With a history of the last 16 numbers, what is the probability of:
a) one number appearing 3 times
b) two numbers each appearing twice
c) both a) and b), one number appears 3 times and two other numbers appear twice
thanks
March 25th, 2019 at 11:52:57 PM
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Quote: KevinAA. He says there is no way that a number can appear on the board 3 times,
Why is that. Ask him, he won't have
an answer. A practiced dealer might
be able to hit a specific section if
the conditions are right. Hitting
specific numbers consistently is
impossible.
For years I had a 24" wheel like
this one, and I hit the same
number 2 times in a row all
the time, and even 3 in a row
a few times. It's random, the
ball has no memory.
"It's not called gambling if the math is on your side."
March 26th, 2019 at 2:43:50 AM
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Quote: KevinAAI know of someone who believes the dealer manipulates the wheel and ball spin to produce duplicates. He says there is no way that a number can appear on the board 3 times, or two numbers on the board twice each (or certainly both) without the dealer manipulating the wheel and ball spin. I say this is bogus but I would like to have probabilities (if they aren't that low, which I suspect) to prove him wrong.
With a history of the last 16 numbers, what is the probability of:
a) one number appearing 3 times
b) two numbers each appearing twice
c) both a) and b), one number appears 3 times and two other numbers appear twice
thanks
On both my Roulette App and in real life Roulette, I have had the triple number Combo happen. On my Roulette App. 21 21 21. 21 21 21. Separate times. In real life. 5 5 5. 5 5 5. Separate times. :) I'm with your friend on this one. :)
In both The Hunger Games and in gambling, may the odds be ever in your favor. :D
"Man Babes" #AxelFabulous
"Olive oil is processed but it only has one
ingredient, olive oil."-Even Bob, March 27/28th. :D The 2 year war is over! Woo-hoo! :D
I sometimes speak in metaphors. ;) Remember this. ;)
Crack the code. :D 8.9.13.25.14.1.13.5.9.19.14.1.20.8.1.14! :D
"For about the 4096th time, let me offer a radical idea to those of you who don't like Nathan -- block her and don't visit Nathan's Corner. What is so complicated about it?" Wizard, August 21st. :D
March 26th, 2019 at 1:16:24 PM
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Quote: KevinAAWith a history of the last 16 numbers, what is the probability of:
edit
see below postLast edited by: 7craps on Mar 26, 2019winsome johnny (not Win some johnny)
March 26th, 2019 at 5:56:52 PM
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It looks like you would have to jump through some hoops to get a calculated answer, but I did some quick simulations, and after 25 million runs of 16 spins (on a double-zero) wheel, I got a surprising answer:
You get at least one number showing up three or more times 27.5% of the time
You get at least two numbers showing up two or more times 81.8% of the time
You get both in the same 16 spins 24.7% of the time
(Clarification: this is the probability of one number appearing three or more times and another appearing at least twice)
That first number looks a little high to me...
The second one, however, makes a little sense; even if the first 14 spins are 14 different numbers, the probability of the 15th spin matching one of them is 7/19, or about 37%, and the probability of the last number matching any of the other 13 is 13/38.
You get at least one number showing up three or more times 27.5% of the time
You get at least two numbers showing up two or more times 81.8% of the time
You get both in the same 16 spins 24.7% of the time
(Clarification: this is the probability of one number appearing three or more times and another appearing at least twice)
That first number looks a little high to me...
The second one, however, makes a little sense; even if the first 14 spins are 14 different numbers, the probability of the 15th spin matching one of them is 7/19, or about 37%, and the probability of the last number matching any of the other 13 is 13/38.
Last edited by: ThatDonGuy on Mar 26, 2019
March 26th, 2019 at 6:27:15 PM
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I only ran 100k simsQuote: ThatDonGuyIt looks like you would have to jump through some hoops to get a calculated answer, but I did some quick simulations, and after 25 million runs of 16 spins (on a double-zero) wheel, I got a surprising answer:
You get at least one number showing up three or more times 27.5% of the time
since 2 programs of mine (Winstats and excel) were in a very close agreement only after 10k sims
that value (27.5% ) looks like it could be the average number of numbers that hit 3 times
in Excel
=BINOMDIST(3,16,1/38,0)*38 = 0.2742
I ran out of time with that.
I agree the calculation would be a challenge to pull off.
I am sure someone has done it
at least our results show the OP what he is after
added:
ok, I had some code wrong in my sim
(Thought I did it a different way. was only checking 3 and not 3 or more and 2 and not 2 or more)
Don results(x%)
a)0.27788 (27.5%)
b)0.81953 (81.8%)
c)0.24546 (24.7%)
in agreement now
Last edited by: 7craps on Mar 26, 2019
winsome johnny (not Win some johnny)
March 26th, 2019 at 6:56:23 PM
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Quote: 7crapsI agree the calculation would be a challenge to pull off.
I am sure someone has done it
at least our results show the OP what he is after
It's not "difficult" so much as it is time consuming; I think what needs to be done is, every combination of "hits" that add up to 16 need to be determined, calculated separately, and then added.
For example:
{16} - 1 number comes up 16 times
{15, 1} - 1 comes up 15 times; another comes up once
{14, 2} - 1 comes up 14 times; another comes up twice
{14, 1, 1} - 1 comes up 14 times; two others come up once
and so on
March 27th, 2019 at 4:06:29 PM
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After some serious number crunching, I got some exact numbers (note the assumptions made are different from the ones I made earlier concerning what counts as "two numbers coming up twice"):
There are 3816 = (deep inhale) 18,903,296,479,567,620,845,142,016 different sets of numbers in 16 spins of a double-zero wheel
Of these:
5,207,779,573,032,238,911,126,016, or about 27.55%, of them have at least one number appear three or more times
10,802,426,009,482,612,080,576,000, or about 57.15%, of them have no number appear three or more times, but two or more numbers appear twice
2,902,218,716,192,061,254,510,808, or about 15.35%, of them have at least one number appear three or more times and two other numbers appear at least twice
There are 3816 = (deep inhale) 18,903,296,479,567,620,845,142,016 different sets of numbers in 16 spins of a double-zero wheel
Of these:
5,207,779,573,032,238,911,126,016, or about 27.55%, of them have at least one number appear three or more times
10,802,426,009,482,612,080,576,000, or about 57.15%, of them have no number appear three or more times, but two or more numbers appear twice
2,902,218,716,192,061,254,510,808, or about 15.35%, of them have at least one number appear three or more times and two other numbers appear at least twice
March 27th, 2019 at 4:54:10 PM
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Quote: ThatDonGuy
You get at least one number showing up three or more times 27.5% of the time
Just look at some roulette tote
boards in the casino. One number
is usually hot, often more than
one.
Because roulette is random, you
can't look at what just one wheel
is producing. To get an useful
statistic you'd have to look at every
roulette wheel in the world at
the same time. That's where it all
even's out.
"It's not called gambling if the math is on your side."
March 27th, 2019 at 5:27:34 PM
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This makes for a pretty good math problem, but the answer will help nobody lose less money in roulette.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
March 27th, 2019 at 6:42:35 PM
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The interesting thing I see about this with the large history boards, who actually looks at the numbers for hitting at least 2 times or 3 times? and how fast can they spot it?Quote: KevinAAHe says there is no way that a number can appear on the board 3 times, or two numbers on the board twice each (or certainly both) without the dealer manipulating the wheel and ball spin.
I say this is bogus
Just a glance at 16 numbers, without a streak for 2, I say it is not that easy to instantly spot the repeaters.
15
2
35
5
19
4
13
20
10
19
2
14
0
35
23
1
I would think more would see the streaks of 2 and question if the Dealer did that (of course the board can malfunction and show lots of streaks)
for example, your favorite number can come up 2 times in a row over 16 spins about 1 in 100 (0.010097111)
but ANY number 2 times in a row over 16 spins is almost 1 in 3 (0.329695845)
3 in a row is more difficult and could point to a Dealer, if you believe, that makes it happen.
your favorite number can come up at least 3 times in a row over 16 spins about 1 in 4,018
ANY number at least 3 times in a row over 16 spins is almost 1 in 106
The casinos 'hit it big' when they started to place history boards at the Roulette tables.
winsome johnny (not Win some johnny)
March 27th, 2019 at 7:22:18 PM
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Taken by itself, every roulette wheel is a rogue
wheel. Anything could happen & it sometimes
does. You have to look at hundreds and
thousands of wheels at once before any
of the probability makes sense.
wheel. Anything could happen & it sometimes
does. You have to look at hundreds and
thousands of wheels at once before any
of the probability makes sense.
"It's not called gambling if the math is on your side."
March 28th, 2019 at 10:22:36 AM
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This is the "birthday problem", just like finding the probability of three matches with 38 total days and 16 people.
I found a formula for triples...it's 1 minus the sum from i=0 to n/2 of:
m!n!/ (i! (n - 2i)! (m - n + i)! * 2^i * m^n)
Where m=38 and n=16.
27.55%.
I found a formula for triples...it's 1 minus the sum from i=0 to n/2 of:
m!n!/ (i! (n - 2i)! (m - n + i)! * 2^i * m^n)
Where m=38 and n=16.
27.55%.
It’s all about making that GTA
March 28th, 2019 at 12:19:25 PM
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there seems to be a lack of a generalized formula for these type of questions.Quote: Ace2This is the "birthday problem", just like finding the probability of three matches with 38 total days and 16 people.
I found a formula for triples...it's 1 minus the sum from i=0 to n/2 of:
m!n!/ (i! (n - 2i)! (m - n + i)! * 2^i * m^n)
Where m=38 and n=16.
27.55%.
I have NOT searched this much.
Nice find. Most just simulate it.
I doubt 1 in 1,000 can understand what is going on in the formula.
I have this using pari/gp
m=38;
n=16;
x=sum(k=0,floor(n/2),(m!*n!/(k!*(n-2*k)!*(m-n+k)!*2^k*m^n)));
x
y=1-x;
y
returns
535339183083083769647/1943184259823974182272
as a decimal
0.27549584162007268958057372875293915562 (on my machine)
Last edited by: 7craps on Mar 28, 2019
winsome johnny (not Win some johnny)
March 28th, 2019 at 7:43:56 PM
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an updateQuote: Ace2This is the "birthday problem", just like finding the probability of three matches with 38 total days and 16 people.
I found a formula for triples...it's 1 minus the sum from i=0 to n/2 of:
m!n!/ (i! (n - 2i)! (m - n + i)! * 2^i * m^n)
Where m=38 and n=16.
27.55%.
the above formula found here (along with others)
https://math.stackexchange.com/questions/25876/probability-of-3-people-in-a-room-of-30-having-the-same-birthday
looks to have some issues, to me,
has a terrible time with rolling one Die and getting one number 3 times
m=6
n=9 (for example)
(m - n + i)! = 6-9+0 = (-3)!
back to being interesting
winsome johnny (not Win some johnny)
March 28th, 2019 at 8:38:31 PM
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Quote: 7craps
returns
535339183083083769647/1943184259823974182272
That matches the fraction I got, although yours is in lowest terms (divide both numerator and denominator of mine by 9728)
March 28th, 2019 at 8:56:14 PM
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yes it does.Quote: ThatDonGuyThat matches the fraction I got, although yours is in lowest terms (divide both numerator and denominator of mine by 9728)
I did check that.
the formula Ace2 found will be difficult to use when the number of spins gets above 38
in our example here.
(-x)! just does not compute
gp > m=38;
gp > n=39;
gp > x=sum(k=0,floor(n/2),(m!*n!/(k!*(n-2*k)!*(m-n+k)!*2^k*m^n)));
*** at top-level: .../2),(m!*n!/(k!*(n-2*k)!*(m-n+k)!*2^k*m^n)))
*** _!: domain error in factorial: argument < 0
I will have to look more at your method.
or at some other methods that are out there.
A Markov chain gets quickly out-of-hand with the number of states, but looks doable.
but for now
MLB, NCAAB, NBA time!
winsome johnny (not Win some johnny)
March 29th, 2019 at 1:33:57 AM
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Here’s a close approximation I derived.
The average number of spins needed to hit any number you choose is 38, so in 15.5 spins (half point adjustment) we expect 15.5/38 occurrences of selected number. Adding in ever-useful Poisson, we can say the probability of all 38 numbers having less than 3 occurrences after 15.5 spins is:
1 - [((15.5/38)^2 / 2 + 15.5/38 + 1) / e^(15.5/38)] ^38 = 27.30 %, within 20 basis points of 27.55.
I believe there is also an exact, simple-formula calculus solution to this. Working on it.
The average number of spins needed to hit any number you choose is 38, so in 15.5 spins (half point adjustment) we expect 15.5/38 occurrences of selected number. Adding in ever-useful Poisson, we can say the probability of all 38 numbers having less than 3 occurrences after 15.5 spins is:
1 - [((15.5/38)^2 / 2 + 15.5/38 + 1) / e^(15.5/38)] ^38 = 27.30 %, within 20 basis points of 27.55.
I believe there is also an exact, simple-formula calculus solution to this. Working on it.
It’s all about making that GTA
March 29th, 2019 at 8:05:13 AM
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NiceQuote: Ace2Here’s a close approximation I derived.
I found some Mathematica code that is very nice. uses multinomial distribution
The author ported it to R
and R does ok, except when rounding to a very small number (no arbitrary precision in base R)
Here is to 77 spins for 3 times
prob YES for 77 == 1
the others below 77 for YES are shown as 1 but are not (close)
NO YES (cdf)
0 1 0
1 1 0
2 1 0
3 0.999307 0.000692521
4 0.997285 0.00271541
5 0.993345 0.00665472
6 0.986957 0.0130428
7 0.977647 0.0223528
8 0.965009 0.0349911
9 0.948712 0.0512875
10 0.928514 0.0714863
11 0.904264 0.0957359
12 0.875918 0.124082
13 0.843539 0.156461
14 0.807302 0.192698
15 0.767493 0.232507
16 0.724504 0.275496
17 0.678824 0.321176
18 0.631024 0.368976
19 0.581741 0.418259
20 0.531656 0.468344
21 0.481472 0.518528
22 0.431887 0.568113
23 0.383572 0.616428
24 0.337145 0.662855
25 0.293153 0.706847
26 0.252051 0.747949
27 0.214194 0.785806
28 0.179825 0.820175
29 0.149079 0.850921
30 0.121983 0.878017
31 0.0984651 0.901535
32 0.0783695 0.92163
33 0.0614703 0.93853
34 0.04749 0.95251
35 0.0361172 0.963883
36 0.0270239 0.972976
37 0.0198811 0.980119
38 0.014372 0.985628
39 0.0102022 0.989798
40 0.00710663 0.992893
41 0.00485422 0.995146
42 0.00324883 0.996751
43 0.00212883 0.997871
44 0.00136456 0.998635
45 0.000854855 0.999145
46 0.000522915 0.999477
47 0.000312012 0.999688
48 0.000181404 0.999819
49 0.00010265 0.999897
50 5.64648e-05 0.999944
51 3.0153e-05 0.99997
52 1.56099e-05 0.999984
53 7.82201e-06 0.999992
54 3.78762e-06 0.999996
55 1.76911e-06 0.999998
56 7.95473e-07 0.999999
57 3.43583e-07 1
58 1.42211e-07 1
59 5.62563e-08 1
60 2.1206e-08 1
61 7.59179e-09 1
62 2.57153e-09 1
63 8.20601e-10 1
64 2.4548e-10 1
65 6.84456e-11 1
66 1.76676e-11 1
67 4.18796e-12 1
68 9.0272e-13 1
69 1.74802e-13 1
70 2.99406e-14 1
71 4.44503e-15 1
72 5.56288e-16 1
73 5.63592e-17 1
74 4.33533e-18 1
75 2.25173e-19 1
76 5.9256e-21 1
77 0 1
> end.time <- Sys.time()
> print(end.time - start.time)
Time difference of 0.734354 secs
I can post the R code and link to webpage as soon as I clean it all up (or down)
Last edited by: 7craps on Mar 29, 2019
winsome johnny (not Win some johnny)
March 29th, 2019 at 9:21:00 AM
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Quote: 7crapsthe formula Ace2 found will be difficult to use when the number of spins gets above 38
in our example here.
(-x)! just does not compute
I will have to look more at your method.
Well, there's always .NET's BigInteger class; you can "pre-build" an array of factorials to speed things up.
First, generate a list of all distinct ways to partition N (= the number of spins) items.
There may be a faster way of doing it, but what I did was:
(a) Start with the 1-element set {N}; this represents all N spins being the same number
(b) Find the rightmost number in the most recent set > 1; reduce it by 1, then add the reduced number to the set as many times as possible until the sum >= N, then, if the sum < N, add the difference to the set
For example, with N = 5, you get {5}, then {4 1}, then {3 2}, then {3 1 1}, then {2 2 1}, then {2 1 1 1}, and finally {1 1 1 1 1}
Each set represents the number of "groups" of numbers. For example, {12 3 1} is one number appearing 12 times, one appearing 3 times, and one appearing once.
For each set, calculate the number of ways it can be obtained:
Divide N! by the product of the factorials of the numbers in each set (so, for {12, 3, 1}, start with 16! / (12! 3! 1!)).
This is the number of permutations of, say, 16 balls, where 12 are red, 3 are blue, and 1 is green.
Now, there are 38 possible values for the first number, 37 for the second, and so on, but for each number that appears K times in the set, divide the result by K! to take into account the fact that you are counting the same numbers multiple times but in a different order.
Clarification: for N = 4, the {2 2} set has six permutations - AABB, ABAB, BAAB, ABBA, BABA, and BBAA. A can be any number from 1 to 38, and B can be any number from 1 to 38 other than A, so (A,B) can be both (2,9) and (9,2), but you are then counting spin set (2, 9, 9, 2) as both ABBA fo (2,9) and BAAB for (9,2).
Example: for N = 10, {3, 2, 2, 1, 1, 1} is a set of spins that has six different numbers appear.
There are 10! / (3! 2! 2! 1! 1! 1!} = 151,200 ways to permute the six different numbers.
There are 38 possible numbers for the first one (the one that appears 3 times), 37 for the second, 36, for the third, ..., 33 for the sixth.
However, there are two numbers that appear twice and three that appear once, so multiply 151,200 by 38 x 37 x 36 x 35 x 34 x 33 and then divide by (2! x 3!).
March 29th, 2019 at 10:52:24 AM
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Sorry to get emotional, but this is one of my favorite things about math...there are so many different ways to approach and solve the same problem. Wiping a tear now .
It’s all about making that GTA
March 29th, 2019 at 11:07:26 AM
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I hadn’t thought about that. I found that formula looking for birthday triple solutions, so I assume it was derived in the spirit of the original birthday problem which deals with pairs. And in that case n would never go higher than m since it’s impossible to, for example, select 380 dates from 365 and not have a pair. But it will happen with triples.Quote: 7crapsthe formula Ace2 found will be difficult to use when the number of spins gets above 38
in our example here.
(-x)! just does not compute
It’s all about making that GTA
March 29th, 2019 at 11:40:50 AM
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I have that exact formula in a paperQuote: Ace2I hadn’t thought about that. I found that formula looking for birthday triple solutions, so I assume it was derived in the spirit of the original birthday problem which deals with pairs.
"The matching, birthday and the strong birthday
problem: a contemporary review"
Anirban DasGupta
Had it for some time.
Started and finished a Markov chain solution for the 'classical birthday problem'
but for 3+ matches it gets tiring for me.
and it can bog down the program with many states
n*(n*1)/2 (familiar)
PLUS n+2
so 365*366/2 + 365+2 = 67,162 states for at least 3 sharing the same BDay
00 Roulette has only 781 states (R and Excel handle that just fine)
and one Die has just 29 states. I did that one 1st.
The R code I found/adjusted (from Mathematica) duplicates it (1d6 - one Die) just fine
(only 43 lines of code)
NO YES (cdf)
0 1 0
1 1 0
2 1 0
3 0.972222 0.0277778
4 0.902778 0.0972222
5 0.787037 0.212963
6 0.632716 0.367284
7 0.459105 0.540895
8 0.292567 0.707433
9 0.157536 0.842464
10 0.0675154 0.932485
11 0.0206297 0.97937
12 0.00343829 0.996562
13 0 1
> end.time <- Sys.time()
> print(end.time - start.time)
Time difference of 0.7343569 secs
from Excel
| roll | cdf | |
|---|---|---|
| 3 | 0.027777778 | 0.027777778 |
| 4 | 0.069444444 | 0.097222222 |
| 5 | 0.115740741 | 0.212962963 |
| 6 | 0.154320988 | 0.367283951 |
| 7 | 0.173611111 | 0.540895062 |
| 8 | 0.166538066 | 0.707433128 |
| 9 | 0.135030864 | 0.842463992 |
| 10 | 0.090020576 | 0.932484568 |
| 11 | 0.046885717 | 0.979370285 |
| 12 | 0.017191429 | 0.996561714 |
| 13 | 0.003438286 | 1 |
I also agree, sometimes it feels good to know there is more than 1 way to get the right answer.
I have seen a few closed-form methods, but so far they only work for a specific problem, not all problems
except the R code one I have. So far so good.
Now to figure out what I want to do with it.
Last edited by: 7craps on Mar 29, 2019
winsome johnny (not Win some johnny)
March 30th, 2019 at 12:57:27 AM
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Just curious...then why didn’t you use it before I did? I’d never seen it before yesterday, never had a need for that formula.Quote: 7crapsI have that exact formula in a paper
"The matching, birthday and the strong birthday
problem: a contemporary review"
Anirban DasGupta
Had it for some time.
It’s all about making that GTA
March 30th, 2019 at 3:12:00 AM
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Sorry to be late to the party, but if the question is what is the probability that there will be at least one birthday common to three or more people out of n people, I get the following:
Excel crashes after 118 as the numbers get too big.
So, with 88 people there is more than a 51.1% chance that three or more people will share the same birthday.
I did this in Excel, but this seems to be the general formula:
Probability there will NOT be a birthday common to three or more people = (fact(n)/365^n)*[sum for d = 0 to int(n/2)] of combin(365,d)*combin(365-d,n-2d)/2^d. Note that d represents the number of days shared by exactly two people.
| People | No Triple | Triple |
|---|---|---|
| 3 | 0.999992 | 0.000008 |
| 4 | 0.999970 | 0.000030 |
| 5 | 0.999925 | 0.000075 |
| 6 | 0.999851 | 0.000149 |
| 7 | 0.999739 | 0.000261 |
| 8 | 0.999584 | 0.000416 |
| 9 | 0.999377 | 0.000623 |
| 10 | 0.999112 | 0.000888 |
| 11 | 0.998782 | 0.001218 |
| 12 | 0.998379 | 0.001621 |
| 13 | 0.997898 | 0.002102 |
| 14 | 0.997330 | 0.002670 |
| 15 | 0.996671 | 0.003329 |
| 16 | 0.995912 | 0.004088 |
| 17 | 0.995047 | 0.004953 |
| 18 | 0.994071 | 0.005929 |
| 19 | 0.992976 | 0.007024 |
| 20 | 0.991757 | 0.008243 |
| 21 | 0.990408 | 0.009592 |
| 22 | 0.988922 | 0.011078 |
| 23 | 0.987295 | 0.012705 |
| 24 | 0.985519 | 0.014481 |
| 25 | 0.983591 | 0.016409 |
| 26 | 0.981503 | 0.018497 |
| 27 | 0.979253 | 0.020747 |
| 28 | 0.976833 | 0.023167 |
| 29 | 0.974240 | 0.025760 |
| 30 | 0.971469 | 0.028531 |
| 31 | 0.968516 | 0.031484 |
| 32 | 0.965376 | 0.034624 |
| 33 | 0.962046 | 0.037954 |
| 34 | 0.958521 | 0.041479 |
| 35 | 0.954798 | 0.045202 |
| 36 | 0.950874 | 0.049126 |
| 37 | 0.946746 | 0.053254 |
| 38 | 0.942411 | 0.057589 |
| 39 | 0.937867 | 0.062133 |
| 40 | 0.933111 | 0.066889 |
| 41 | 0.928141 | 0.071859 |
| 42 | 0.922956 | 0.077044 |
| 43 | 0.917554 | 0.082446 |
| 44 | 0.911935 | 0.088065 |
| 45 | 0.906097 | 0.093903 |
| 46 | 0.900040 | 0.099960 |
| 47 | 0.893764 | 0.106236 |
| 48 | 0.887269 | 0.112731 |
| 49 | 0.880556 | 0.119444 |
| 50 | 0.873625 | 0.126375 |
| 51 | 0.866478 | 0.133522 |
| 52 | 0.859115 | 0.140885 |
| 53 | 0.851540 | 0.148460 |
| 54 | 0.843754 | 0.156246 |
| 55 | 0.835759 | 0.164241 |
| 56 | 0.827559 | 0.172441 |
| 57 | 0.819156 | 0.180844 |
| 58 | 0.810555 | 0.189445 |
| 59 | 0.801758 | 0.198242 |
| 60 | 0.792770 | 0.207230 |
| 61 | 0.783595 | 0.216405 |
| 62 | 0.774239 | 0.225761 |
| 63 | 0.764706 | 0.235294 |
| 64 | 0.755001 | 0.244999 |
| 65 | 0.745131 | 0.254869 |
| 66 | 0.735101 | 0.264899 |
| 67 | 0.724918 | 0.275082 |
| 68 | 0.714587 | 0.285413 |
| 69 | 0.704117 | 0.295883 |
| 70 | 0.693513 | 0.306487 |
| 71 | 0.682783 | 0.317217 |
| 72 | 0.671934 | 0.328066 |
| 73 | 0.660974 | 0.339026 |
| 74 | 0.649912 | 0.350088 |
| 75 | 0.638754 | 0.361246 |
| 76 | 0.627509 | 0.372491 |
| 77 | 0.616186 | 0.383814 |
| 78 | 0.604793 | 0.395207 |
| 79 | 0.593338 | 0.406662 |
| 80 | 0.581831 | 0.418169 |
| 81 | 0.570280 | 0.429720 |
| 82 | 0.558693 | 0.441307 |
| 83 | 0.547080 | 0.452920 |
| 84 | 0.535450 | 0.464550 |
| 85 | 0.523812 | 0.476188 |
| 86 | 0.512174 | 0.487826 |
| 87 | 0.500545 | 0.499455 |
| 88 | 0.488935 | 0.511065 |
| 89 | 0.477352 | 0.522648 |
| 90 | 0.465804 | 0.534196 |
| 91 | 0.454302 | 0.545698 |
| 92 | 0.442852 | 0.557148 |
| 93 | 0.431463 | 0.568537 |
| 94 | 0.420145 | 0.579855 |
| 95 | 0.408904 | 0.591096 |
| 96 | 0.397748 | 0.602252 |
| 97 | 0.386686 | 0.613314 |
| 98 | 0.375725 | 0.624275 |
| 99 | 0.364873 | 0.635127 |
| 100 | 0.354135 | 0.645865 |
| 101 | 0.343520 | 0.656480 |
| 102 | 0.333033 | 0.666967 |
| 103 | 0.322682 | 0.677318 |
| 104 | 0.312471 | 0.687529 |
| 105 | 0.302407 | 0.697593 |
| 106 | 0.292495 | 0.707505 |
| 107 | 0.282740 | 0.717260 |
| 108 | 0.273147 | 0.726853 |
| 109 | 0.263721 | 0.736279 |
| 110 | 0.254464 | 0.745536 |
| 111 | 0.245381 | 0.754619 |
| 112 | 0.236475 | 0.763525 |
| 113 | 0.227749 | 0.772251 |
| 114 | 0.219205 | 0.780795 |
| 115 | 0.210845 | 0.789155 |
| 116 | 0.202670 | 0.797330 |
| 117 | 0.194681 | 0.805319 |
| 118 | 0.186879 | 0.813121 |
Excel crashes after 118 as the numbers get too big.
So, with 88 people there is more than a 51.1% chance that three or more people will share the same birthday.
I did this in Excel, but this seems to be the general formula:
Probability there will NOT be a birthday common to three or more people = (fact(n)/365^n)*[sum for d = 0 to int(n/2)] of combin(365,d)*combin(365-d,n-2d)/2^d. Note that d represents the number of days shared by exactly two people.
Last edited by: Wizard on Mar 30, 2019
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
March 30th, 2019 at 7:05:15 AM
permalink
The OP Q is about 00 Roulette, but yours looks fine.Quote: WizardSorry to be late to the party, but if the question is what is the probability that there will be at least one birthday common to three or more people out of n people, I get the following:
Using some R code I get this in about 4 seconds
again the ''1 is the YES column starting at 341 is rounded up
R loses precision as does Excel
> print(formatC(cbind(no,yes),digits=15),quote=0)
NO YES (cdf)
0 1 0
1 1 0
2 1 0
3 0.999992493901296 7.50609870370234e-06
4 0.999970037299143 2.9962700856645e-05
5 0.999925247144711 7.47528552890175e-05
6 0.999850801970449 0.000149198029551267
7 0.999739442662695 0.000260557337304679
8 0.999583973765641 0.000416026234358879
9 0.9993772653009 0.000622734699099903
10 0.999112255086985 0.000887744913014799
11 0.998781951542923 0.00121804845707663
12 0.998379436960072 0.00162056303992786
13 0.997897871225946 0.00210212877405402
14 0.997330495983503 0.00266950401649713
15 0.99667063920893 0.00332936079107005
16 0.995911720190446 0.00408827980955362
17 0.995047254890109 0.00495274510989108
18 0.99407086166994 0.00592913833006004
19 0.992976267363005 0.00702373263699485
20 0.991757313669426 0.00824268633057368
21 0.990407963856433 0.00959203614356652
22 0.988922309740811 0.0110776902591893
23 0.987294578931258 0.0127054210687415
24 0.985519142307365 0.0144808576926347
25 0.983590521710933 0.0164094782890674
26 0.981503397824651 0.0184966021753487
27 0.979252618212152 0.0207473817878476
28 0.976833205492652 0.0231667945073485
29 0.974240365622576 0.0257596343774237
30 0.971469496255676 0.0285305037443235
31 0.968516195152444 0.0314838048475563
32 0.965376268608808 0.0346237313911922
33 0.962045739873464 0.0379542601265361
34 0.958520857522492 0.0414791424775082
35 0.954798103759361 0.0452018962406394
36 0.950874202607908 0.0491257973920917
37 0.946746127965475 0.0532538720345247
38 0.942411111482901 0.0575888885170989
39 0.93786665023804 0.0621333497619601
40 0.933110514169072 0.0668894858309279
41 0.928140753233972 0.0718592467660281
42 0.922955704262497 0.0770442957375032
43 0.917553997467214 0.0824460025327861
44 0.91193456258039 0.0880654374196099
45 0.906096634583979 0.0939033654160205
46 0.900039759000467 0.0999602409995327
47 0.893763796713001 0.106236203286999
48 0.887268928284118 0.112731071715882
49 0.880555657743166 0.119444342256834
50 0.87362481581382 0.12637518418618
51 0.866477562554109 0.133522437445891
52 0.859115389382908 0.140884610617092
53 0.851540120468234 0.148459879531766
54 0.843753913454424 0.156246086545576
55 0.835759259506983 0.164240740493017
56 0.827558982655904 0.172441017344096
57 0.819156238420174 0.180843761579826
58 0.810554511698505 0.189445488301495
59 0.801757613913476 0.198242386086524
60 0.792769679398813 0.207230320601187
61 0.783595161021965 0.216404838978035
62 0.774238825036683 0.225761174963317
63 0.764705745163194 0.235294254836806
64 0.755001295896118 0.244998704103882
65 0.745131145043274 0.254868854956726
66 0.735101245501294 0.264898754498706
67 0.724917826277039 0.275082173722961
68 0.714587382766632 0.285412617233368
69 0.704116666307026 0.295883333692974
70 0.693512673017964 0.306487326982036
71 0.68278263195513 0.31721736804487
72 0.671933992598355 0.328066007401645
73 0.660974411701514 0.339025588298486
74 0.649911739533737 0.350088260466263
75 0.638754005544217 0.361245994455783
76 0.627509403485722 0.372490596514278
77 0.616186276034429 0.383813723965571
78 0.604793098946192 0.395206901053808
79 0.593338464791722 0.406661535208278
80 0.581831066315392 0.418168933684608
81 0.570279679464325 0.429720320535675
82 0.558693146136422 0.441306853863578
83 0.547080356697526 0.452919643302474
84 0.535450232319587 0.464549767680413
85 0.523811707192771 0.476188292807229
86 0.512173710665682 0.487826289334318
87 0.500545149368595 0.499454850631405
88 0.488934889375264 0.511065110624736
89 0.477351738459167 0.522648261540833
90 0.465804428500194 0.534195571499806
91 0.454301598097667 0.545698401902333
92 0.442851775445099 0.557148224554902
93 0.43146336152156 0.56853663847844
94 0.420144613653521 0.579855386346479
95 0.408903629499958 0.591096370500042
96 0.397748331512055 0.602251668487945
97 0.386686451917207 0.613313548082793
98 0.375725518275139 0.624274481724861
99 0.364872839651866 0.635127160348134
100 0.354135493454824 0.645864506545176
101 0.343520312970045 0.656479687029955
102 0.333033875639397 0.666966124360603
103 0.322682492113117 0.677317507886883
104 0.312472196109641 0.687527803890359
105 0.302408735111586 0.697591264888414
106 0.292497561923308 0.707502438076693
107 0.282743827111964 0.717256172888036
108 0.273152372350396 0.726847627649604
109 0.263727724676521 0.736272275323479
110 0.25447409168009 0.74552590831991
111 0.24539535762395 0.75460464237605
112 0.236495080503121 0.763504919496879
113 0.22777649004119 0.77222350995881
114 0.219242486619751 0.780757513380249
115 0.210895641132873 0.789104358867127
116 0.202738195754897 0.797261804245103
117 0.194772065606257 0.805227934393743
118 0.186998841298544 0.813001158701456
119 0.17941979233666 0.82058020766334
120 0.172035871352627 0.827964128647372
121 0.164847719142583 0.835152280857417
122 0.157855670475565 0.842144329524435
123 0.151059760639955 0.848940239360045
124 0.144459732690934 0.855540267309066
125 0.138055045359971 0.861944954640029
126 0.131844881585307 0.868155118414693
127 0.125828157620488 0.874171842379512
128 0.120003532676409 0.87999646732359
129 0.11436941905095 0.88563058094905
130 0.108923992699127 0.891076007300873
131 0.103665204195856 0.896334795804144
132 0.0985907900427375 0.901409209957262
133 0.093698284269946 0.906301715730054
134 0.0889850302841706 0.911014969715829
135 0.0844481929136682 0.915551807086332
136 0.0800847706018735 0.919915229398127
137 0.0758916077015916 0.924108392298408
138 0.0718654068226394 0.928134593177361
139 0.068002741186833 0.931997258813167
140 0.0643000669454871 0.935699933054513
141 0.0607537354160062 0.939246264583994
142 0.0573600051957981 0.942639994804202
143 0.0541150541135216 0.945884945886478
144 0.0510149909796238 0.948985009020376
145 0.0480558671002083 0.951944132899792
146 0.0452336875204807 0.954766312479519
147 0.0425444219663277 0.957455578033672
148 0.0399840154549807 0.960015984545019
149 0.0375483985481934 0.962451601451807
150 0.0352334972238851 0.964766502776115
151 0.0330352423447696 0.96696475765523
152 0.030949578705077 0.969050421294923
153 0.0289724736390725 0.971027526360927
154 0.0270999251776604 0.97290007482234
155 0.0253279697419245 0.974672030258075
156 0.0236526893649786 0.976347310635021
157 0.0220702184359745 0.977929781564026
158 0.0205767499625127 0.979423250037487
159 0.0191685413500388 0.980831458649961
160 0.0178419196990408 0.982158080300959
161 0.0165932866230099 0.98340671337699
162 0.0154191225921547 0.984580877407845
163 0.014315990809785 0.985684009190215
164 0.0132805406300731 0.986719459369927
165 0.0123095105275695 0.98769048947243
166 0.0113997306303909 0.988600269369609
167 0.0105481248303909 0.989451875169609
168 0.0097517124848938 0.990248287515106
169 0.00900760972569064 0.990992390274309
170 0.00831303039197616 0.991686969608024
171 0.00766528660475483 0.992334713395245
172 0.00706178900094211 0.992938210999058
173 0.00650004664596247 0.993499953354038
174 0.0059776666440797 0.99402233335592
175 0.00549235346600646 0.994507646533994
176 0.00504190801352618 0.994958091986474
177 0.00462422644092971 0.99537577355907
178 0.0042372987530251 0.995762701246975
179 0.0038792071993317 0.996120792800668
180 0.00354812448382122 0.996451875516179
181 0.00324231180923165 0.996757688190768
182 0.00296011677455581 0.997039883225444
183 0.0026999711438083 0.997300028856192
184 0.0024603885036064 0.997539611496394
185 0.00223996182647224 0.997760038173528
186 0.00203736095608083 0.997962639043919
187 0.0018513300299515 0.998148669970048
188 0.00168068485431446 0.998319315145686
189 0.0015243102450874 0.998475689754913
190 0.00138115734807691 0.998618842651923
191 0.00125024095068252 0.998749759049318
192 0.00113063679653349 0.998869363203467
193 0.00102147891363651 0.998978521086364
194 0.000921956965762646 0.999078043034237
195 0.000831313635957877 0.999168686364042
196 0.000748842050230381 0.99925115794977
197 0.000673883248652526 0.999326116751348
198 0.000605823710320444 0.99939417628968
199 0.00054409293784372 0.999455907062156
200 0.000488161106294257 0.999511838893706
201 0.000437536780829975 0.99956246321917
202 0.000391764706528403 0.999608235293472
203 0.000350423673318611 0.999649576326681
204 0.000313124458289355 0.999686875541711
205 0.000279507847077822 0.999720492152922
206 0.000249242735507717 0.999750757264492
207 0.000222024312148047 0.999777975687852
208 0.000197572322004904 0.999802427677995
209 0.000175629411137906 0.999824370588862
210 0.000155959551609967 0.99984404044839
211 0.000138346545833237 0.999861653454167
212 0.000122592609064433 0.999877407390936
213 0.000108517028528226 0.999891482971472
214 9.59548974066694e-05 0.999904045102593
215 8.47559217243126e-05 0.999915244078276
216 7.47832979812653e-05 0.999925216702019
217 6.59126592382618e-05 0.999934087340762
218 5.80310872371413e-05 0.999941968912763
219 5.10361880452974e-05 0.999948963811955
220 4.48352286417488e-05 0.999955164771358
221 3.93443318137787e-05 0.999960655668186
222 3.4487726704732e-05 0.999965512273295
223 3.01970523437808e-05 0.999969802947656
224 2.64107114954971e-05 0.999973589288505
225 2.30732721891912e-05 0.999976926727811
226 2.01349143235042e-05 0.999979865085676
227 1.75509187891099e-05 0.999982449081211
228 1.52811966100147e-05 0.99998471880339
229 1.32898556703992e-05 0.99998671014433
230 1.15448026678601e-05 0.999988455197332
231 1.00173780139528e-05 0.999989982621986
232 8.68202148794408e-06 0.999991317978512
233 7.5159665385017e-06 0.999992484033462
234 6.49896121967396e-06 0.99999350103878
235 5.61301384099109e-06 0.999994386986159
236 4.84216150600578e-06 0.999995157838494
237 4.17225980831353e-06 0.999995827740192
238 3.5907920483729e-06 0.999996409207952
239 3.08669642767244e-06 0.999996913303572
240 2.65020976844207e-06 0.999997349790232
241 2.27272639672457e-06 0.999997727273603
242 1.94667091381811e-06 0.999998053329086
243 1.66538366555572e-06 0.999998334616334
244 1.42301780033251e-06 0.9999985769822
245 1.21444688502167e-06 0.999998785553115
246 1.03518212277534e-06 0.999998964817877
247 8.81298288074424e-07 0.999999118701712
248 7.49367562200332e-07 0.999999250632438
249 6.36400516518062e-07 0.999999363599483
250 5.39793551581567e-07 0.999999460206448
251 4.57282157127298e-07 0.999999542717843
252 3.86899411561946e-07 0.999999613100588
253 3.26939189650093e-07 0.99999967306081
254 2.75923593858602e-07 0.999999724076406
255 2.32574168324223e-07 0.999999767425832
256 1.95786494798243e-07 0.999999804213505
257 1.64607807315899e-07 0.999999835392193
258 1.38217296874152e-07 0.999999861782703
259 1.15908809220598e-07 0.999999884091191
260 9.70756681019371e-08 0.999999902924332
261 8.11973831381798e-08 0.999999918802617
262 6.78280260233266e-08 0.999999932171974
263 5.65860811482352e-08 0.999999943413919
264 4.71455971377472e-08 0.999999952854403
265 3.92284843294043e-08 0.999999960771516
266 3.25978200284741e-08 0.99999996740218
267 2.70520385819545e-08 0.999999972947961
268 2.24198970457519e-08 0.999999977580103
269 1.85561195917167e-08 0.99999998144388
270 1.53376349260254e-08 0.999999984662365
271 1.26603309727936e-08 0.999999987339669
272 1.04362600158808e-08 0.99999998956374
273 8.59123548046343e-09 0.999999991408764
274 7.06276866088782e-09 0.999999992937231
275 5.7983000432931e-09 0.9999999942017
276 4.75368550542202e-09 0.999999995246314
277 3.89190267113539e-09 0.999999996108097
278 3.18194711722498e-09 0.999999996818053
279 2.59789203378389e-09 0.999999997402108
280 2.11808838033387e-09 0.999999997881912
281 1.72448560715311e-09 0.999999998275514
282 1.40205566944585e-09 0.999999998597944
283 1.13830539169915e-09 0.999999998861695
284 9.22864277508483e-10 0.999999999077136
285 7.47136639498975e-10 0.999999999252863
286 6.04008474613788e-10 0.999999999395991
287 4.87600858847853e-10 0.999999999512399
288 3.9306280655238e-10 0.999999999606937
289 3.16397554256159e-10 0.999999999683602
290 2.54317106749931e-10 0.999999999745683
291 2.04120641052277e-10 0.999999999795879
292 1.63593016993453e-10 0.999999999836407
293 1.30920204956993e-10 0.99999999986908
294 1.04618923683158e-10 0.999999999895381
295 8.34781944340872e-11 0.999999999916522
296 6.65108714569698e-11 0.999999999933489
297 5.29135106422244e-11 0.999999999947086
298 4.20331956364817e-11 0.999999999957967
299 3.33401596201502e-11 0.99999999996666
300 2.64052268886163e-11 0.999999999973595
301 2.08812559757938e-11 0.999999999979119
302 1.64878994009483e-11 0.999999999983512
303 1.29991077318879e-11 0.999999999987001
304 1.02329005886952e-11 0.999999999989767
305 8.04300709204542e-12 0.999999999991957
306 6.31204535230163e-12 0.999999999993688
307 4.94596684422646e-12 0.999999999995054
308 3.86953858361023e-12 0.99999999999613
309 3.0226753417047e-12 0.999999999996977
310 2.3574669175999e-12 0.999999999997643
311 1.83577277383193e-12 0.999999999998164
312 1.4272790073986e-12 0.999999999998573
313 1.10793142418373e-12 0.999999999998892
314 8.58674042094213e-13 0.999999999999141
315 6.64435201377131e-13 0.999999999999336
316 5.13314060147461e-13 0.999999999999487
317 3.95928978195049e-13 0.999999999999604
318 3.04896460955475e-13 0.999999999999695
319 2.34415214853259e-13 0.999999999999766
320 1.79934678120581e-13 0.99999999999982
321 1.37891323827218e-13 0.999999999999862
322 1.05499239289848e-13 0.999999999999895
323 8.05840971540817e-14 0.999999999999919
324 6.14517551860289e-14 0.999999999999938
325 4.67844426955612e-14 0.999999999999953
326 3.5558884681955e-14 0.999999999999964
327 2.69818405554146e-14 0.999999999999973
328 2.04394422764905e-14 0.99999999999998
329 1.54574477307746e-14 0.999999999999985
330 1.16701125275617e-14 0.999999999999988
331 8.79585450663396e-15 0.999999999999991
332 6.61826236631201e-15 0.999999999999993
333 4.97130116415554e-15 0.999999999999995
334 3.72780776750412e-15 0.999999999999996
335 2.79056063630444e-15 0.999999999999997
336 2.0853603166529e-15 0.999999999999998
337 1.55567755884357e-15 0.999999999999998
338 1.1585213789728e-15 0.999999999999999
339 8.61254754103878e-16 0.999999999999999
340 6.3914507127726e-16 0.999999999999999
341 4.73483222223227e-16 1
342 3.5014197441364e-16 1
343 2.58473051861659e-16 1
344 1.90464896737712e-16 1
345 1.40100684238049e-16 1
346 1.02869882861462e-16 1
347 7.53973256619963e-17 1
348 5.516204545214e-17 1
349 4.02845492122147e-17 1
350 2.93661741804733e-17 1
351 2.13680024196847e-17 1
352 1.55197646722488e-17 1
353 1.12514356672732e-17 1
354 8.14196605637885e-18 1
355 5.88093108919366e-18 1
356 4.23989651400472e-18 1
357 3.05108057986251e-18 1
358 2.19148363048709e-18 1
359 1.57110705762114e-18 1
360 1.12422482565837e-18 1
361 8.02929177067122e-19 1
362 5.72367285270126e-19 1
363 4.07232718967963e-19 1
364 2.89186230832113e-19 1
365 2.04963446838052e-19 1
366 1.44989260937746e-19 1
367 1.02365264412126e-19 1
368 7.21312520326881e-20 1
369 5.07276938985848e-20 1
370 3.56052674717158e-20 1
371 2.49417858801359e-20 1
372 1.74373972654056e-20 1
373 1.21667124064334e-20 1
374 8.47225297798878e-21 1
375 5.88783038099752e-21 1
376 4.08356018307457e-21 1
377 2.82648380929051e-21 1
378 1.95242550851334e-21 1
379 1.34592051992148e-21 1
380 9.25929347067562e-22 1
381 6.35691321436433e-22 1
382 4.3553313491117e-22 1
383 2.97782433428464e-22 1
384 2.03177846418654e-22 1
385 1.38340540287669e-22 1
386 9.39971815846481e-23 1
387 6.37336571830229e-23 1
388 4.31228908074367e-23 1
389 2.91157691720341e-23 1
390 1.961671935202e-23 1
391 1.31885945356141e-23 1
392 8.84791573042416e-24 1
393 5.92311327304192e-24 1
394 3.9565982467037e-24 1
395 2.63726008363765e-24 1
396 1.75403911980052e-24 1
397 1.16406461780553e-24 1
398 7.70837041603953e-25 1
399 5.09321357568027e-25 1
400 3.35784894473091e-25 1
401 2.20885133001388e-25 1
402 1.44978621844053e-25 1
403 9.49444674216154e-26 1
404 6.20382609253465e-26 1
405 4.04454659920816e-26 1
406 2.63085156051966e-26 1
407 1.70739927400699e-26 1
408 1.10555928632597e-26 1
409 7.14221804946392e-27 1
410 4.60345815408822e-27 1
411 2.96026915792141e-27 1
412 1.89919676525683e-27 1
413 1.21561573980608e-27 1
414 7.76257956259838e-28 1
415 4.94532675418499e-28 1
416 3.14310473751707e-28 1
417 1.99293611743532e-28 1
418 1.26064925165382e-28 1
419 7.95531185746082e-29 1
420 5.0081559777853e-29 1
421 3.14522564200956e-29 1
422 1.97049207136573e-29 1
423 1.23152170454958e-29 1
424 7.67802439689187e-30 1
425 4.77520983900919e-30 1
426 2.96255538325087e-30 1
427 1.83344125789566e-30 1
428 1.13185152132359e-30 1
429 6.96994350246854e-31 1
430 4.28136023104188e-31 1
431 2.62326607078839e-31 1
432 1.60326860042457e-31 1
433 9.77392248394895e-32 1
434 5.94326925790433e-32 1
435 3.60471603608721e-32 1
436 2.18072569038736e-32 1
437 1.31586250339183e-32 1
438 7.91944237460332e-33 1
439 4.75388215785425e-33 1
440 2.84621041451816e-33 1
441 1.69959486318925e-33 1
442 1.0122286616738e-33 1
443 6.01259056338481e-34 1
444 3.56196250339949e-34 1
445 2.104537484481e-34 1
446 1.2401050054943e-34 1
447 7.28768439397622e-35 1
448 4.27114923832418e-35 1
449 2.49642651850564e-35 1
450 1.45514543120049e-35 1
451 8.45867364455059e-36 1
452 4.90344199330117e-36 1
453 2.83463619805751e-36 1
454 1.6341266076981e-36 1
455 9.39421930167623e-37 1
456 5.3853855726295e-37 1
457 3.07856609810634e-37 1
458 1.75489101701895e-37 1
459 9.97507533740695e-38 1
460 5.65380621983471e-38 1
461 3.19535158647255e-38 1
462 1.80070940515233e-38 1
463 1.01183588472435e-38 1
464 5.66907437176736e-39 1
465 3.16697029844126e-39 1
466 1.76400441830618e-39 1
467 9.79655156287459e-40 1
468 5.42448691262773e-40 1
469 2.9946766057585e-40 1
470 1.64831771417033e-40 1
471 9.04535284057948e-41 1
472 4.94877264015372e-41 1
473 2.69929691549168e-41 1
474 1.46783993826664e-41 1
475 7.95747523976314e-42 1
476 4.30064966477496e-42 1
477 2.31712029373523e-42 1
478 1.24455003516236e-42 1
479 6.66375279422142e-43 1
480 3.55681722240077e-43 1
481 1.89249063924655e-43 1
482 1.00375741663461e-43 1
483 5.30688761817712e-44 1
484 2.7967929612003e-44 1
485 1.46920771791472e-44 1
486 7.69310460166928e-45 1
487 4.0152137371198e-45 1
488 2.08880201981331e-45 1
489 1.08307964887812e-45 1
490 5.59745857024659e-46 1
491 2.88324512225623e-46 1
492 1.48021629413674e-46 1
493 7.57381027609105e-47 1
494 3.86226366809716e-47 1
495 1.96290932587538e-47 1
496 9.94218602670402e-48 1
497 5.01856205857229e-48 1
498 2.52455511566752e-48 1
499 1.26558368821249e-48 1
500 6.32251079938622e-49 1
501 3.1475538397669e-49 1
502 1.56147034791225e-49 1
503 7.71904090137849e-50 1
504 3.80236619776636e-50 1
505 1.86636867463895e-50 1
506 9.12821075635112e-51 1
507 4.44846689031806e-51 1
508 2.16004714327981e-51 1
509 1.04504710795951e-51 1
510 5.03755508003863e-52 1
511 2.41939347029108e-52 1
512 1.15767681003683e-52 1
513 5.51891358798083e-53 1
514 2.62117793091068e-53 1
515 1.24024417425806e-53 1
516 5.84624116919643e-54 1
517 2.74533954903867e-54 1
518 1.28426929673947e-54 1
519 5.98477222934125e-55 1
520 2.77818625555999e-55 1
521 1.28465916377072e-55 1
522 5.91722171704326e-56 1
523 2.71482331957316e-56 1
524 1.24065049948302e-56 1
525 5.6471815482256e-57 1
526 2.56022784897015e-57 1
527 1.1560593254107e-57 1
528 5.19907674100272e-58 1
529 2.32866386164871e-58 1
530 1.0387513787708e-58 1
531 4.61456024051374e-59 1
532 2.04151455923873e-59 1
533 8.99430375777528e-60 1
534 3.94607079036777e-60 1
535 1.72398578833843e-60 1
536 7.50003177876347e-61 1
537 3.24894343789929e-61 1
538 1.40139227842152e-61 1
539 6.01872629345041e-62 1
540 2.5737445197926e-62 1
541 1.09579871459176e-62 1
542 4.6450358543339e-63 1
543 1.96032728284859e-63 1
544 8.23640131433582e-64 1
545 3.44511607638193e-64 1
546 1.43454962956524e-64 1
547 5.94648648230024e-65 1
548 2.45372609167348e-65 1
549 1.00785956766503e-65 1
550 4.12068705194451e-66 1
551 1.67695782790546e-66 1
552 6.79273439440252e-67 1
553 2.73857128323116e-67 1
554 1.09887218790756e-67 1
555 4.38834404674327e-68 1
556 1.74409845698934e-68 1
557 6.89833844586591e-69 1
558 2.71523447540761e-69 1
559 1.06351967833749e-69 1
560 4.1451945016076e-70 1
561 1.60764873962157e-70 1
562 6.20397140001e-71 1
563 2.38213358184391e-71 1
564 9.1005007685812e-72 1
565 3.45901381653349e-72 1
566 1.30801257223246e-72 1
567 4.92072117104103e-73 1
568 1.84156572259647e-73 1
569 6.85601142683725e-74 1
570 2.53901756461006e-74 1
571 9.3530564870319e-75 1
572 3.42703626386906e-75 1
573 1.24894851397768e-75 1
574 4.52703917248058e-76 1
575 1.63196492880854e-76 1
576 5.85082342597721e-77 1
577 2.08600471434404e-77 1
578 7.39584831651701e-78 1
579 2.60745713772852e-78 1
580 9.14080932948311e-79 1
581 3.18619229484074e-79 1
582 1.10423243390503e-79 1
583 3.80479502980297e-80 1
584 1.30336210256236e-80 1
585 4.43856424777169e-81 1
586 1.50260143969375e-81 1
587 5.05648766625505e-82 1
588 1.69136631169475e-82 1
589 5.62327592601202e-83 1
590 1.85816054176683e-83 1
591 6.10236274346919e-84 1
592 1.99164656348401e-84 1
593 6.45957866014897e-85 1
594 2.08186067392117e-85 1
595 6.66702733519142e-86 1
596 2.12140276884375e-86 1
597 6.70658174064109e-87 1
598 2.10641059645208e-87 1
599 6.57241110188173e-88 1
600 2.03714567828587e-88 1
601 6.27206498397297e-89 1
602 1.91807304562148e-89 1
603 5.82586620012786e-90 1
604 1.75740103554992e-90 1
605 5.26465700157662e-91 1
606 1.5661433767067e-91 1
607 4.62623995516679e-92 1
608 1.35685211596859e-92 1
609 3.95108770709421e-93 1
610 1.14222646926144e-93 1
611 3.27801011946737e-94 1
612 9.33816438388267e-95 1
613 2.64043831768734e-95 1
614 7.41008930417192e-96 1
615 2.06382490463822e-96 1
616 5.7041743615374e-97 1
617 1.56441243828563e-97 1
618 4.25711781177716e-98 1
619 1.14935144865927e-98 1
620 3.07842814953954e-99 1
621 8.1791805941273e-100 1
622 2.15556014081435e-100 1
623 5.63435721157728e-101 1
624 1.46058265309449e-101 1
625 3.75464064860251e-102 1
626 9.57047147946526e-103 1
627 2.418702823584e-103 1
628 6.06005637809339e-104 1
629 1.50513608698413e-104 1
630 3.70543330539097e-105 1
631 9.04117167273806e-106 1
632 2.18620266575091e-106 1
633 5.23832867849035e-107 1
634 1.243619211905e-107 1
635 2.92502279707354e-108 1
636 6.81509770216052e-109 1
637 1.57278286948183e-109 1
638 3.59477026255056e-110 1
639 8.13635662055367e-111 1
640 1.82345464704451e-111 1
641 4.04589563471123e-112 1
642 8.88661787946631e-113 1
643 1.93199792214109e-113 1
644 4.15690477659613e-114 1
645 8.85055357357426e-115 1
646 1.86444709753898e-115 1
647 3.88552687584082e-116 1
648 8.0095757519182e-117 1
649 1.63292745473284e-117 1
650 3.29199033403519e-118 1
651 6.56174576546514e-119 1
652 1.29295284312854e-119 1
653 2.51814039120785e-120 1
654 4.84664159397903e-121 1
655 9.21708242156584e-122 1
656 1.73166386503009e-122 1
657 3.21347721121029e-123 1
658 5.88911749141549e-124 1
659 1.0656344657305e-124 1
660 1.90356080681547e-125 1
661 3.35614527654735e-126 1
662 5.83905850843366e-127 1
663 1.00226595686926e-127 1
664 1.69694792782455e-128 1
665 2.83337416722614e-129 1
666 4.6643461399766e-130 1
667 7.56880839388582e-131 1
668 1.21034558722952e-131 1
669 1.90690155785305e-132 1
670 2.95918742549474e-133 1
671 4.52195858165362e-134 1
672 6.80254267346082e-135 1
673 1.00712441322858e-135 1
674 1.46701436087654e-136 1
675 2.10180625600528e-137 1
676 2.9608809411633e-138 1
677 4.0999349187636e-139 1
678 5.5784453883628e-140 1
679 7.45549359810539e-141 1
680 9.78379640327894e-142 1
681 1.26020340359853e-142 1
682 1.59258946855083e-143 1
683 1.97386543431106e-144 1
684 2.3982514336177e-145 1
685 2.85522418749268e-146 1
686 3.32927965977357e-147 1
687 3.8002478515382e-148 1
688 4.24426329794602e-149 1
689 4.63540932168926e-150 1
690 4.94794146720539e-151 1
691 5.15887348513382e-152 1
692 5.25060272258928e-153 1
693 5.21318822513229e-154 1
694 5.04589725430437e-155 1
695 4.75771547694501e-156 1
696 4.36666671536125e-157 1
697 3.89798505352389e-158 1
698 3.381385649626e-159 1
699 2.84784536164502e-160 1
700 2.32639091882604e-161 1
701 1.84137903088812e-162 1
702 1.41064220427376e-163 1
703 1.04469335465655e-164 1
704 7.46975911477136e-166 1
705 5.14962808776628e-167 1
706 3.41787030790443e-168 1
707 2.18048045577165e-169 1
708 1.33479013913535e-170 1
709 7.8256087370109e-172 1
710 4.38501756371119e-173 1
711 2.34308835683036e-174 1
712 1.1909266425782e-175 1
713 5.74192722106149e-177 1
714 2.61797942752573e-178 1
715 1.12488299274612e-179 1
716 4.53715213447855e-181 1
717 1.71025868988374e-182 1
718 5.99409206471331e-184 1
719 1.9417480570995e-185 1
720 5.7735899522678e-187 1
721 1.56271814947415e-188 1
722 3.81183819595957e-190 1
723 8.27588713804325e-192 1
724 1.57428665366131e-193 1
725 2.57033470857315e-195 1
726 3.50187011807551e-197 1
727 3.82198048250642e-199 1
728 3.13277088730037e-201 1
729 1.7142352988118e-203 1
730 4.69653506523775e-206 1
731 0 1
> end.time <- Sys.time()
> print(end.time - start.time)
Time difference of 3.831339 secs
slick
FYI,
I was shown this years ago (do not know what it is called or ?)
339
no: 8.61254754103878e-16
yes: 0.999999999999999
for yes: to be more accurate (IF it actually matters)
10-8.61254754103878(X9)-16
(X9)-16 means to move the decimal point 16 places to left
and fill in with 9s
1.38745245896122(X9)-16 is a closer answer than just rounding to 1 or 0.999999999999999
.999999999999999138745245896122
added: for at least X number of matches for the BDay problem
2+: 23,0.507297234323982
3+: 88,0.511065110624736 (87,0.499454850631405)
4+: 187,0.502685373188966
5+: 313,0.501070475849204
6+: 460,0.50244941036937
7+: 623,0.502948948664566 (622,0.499795687887501)
8+: 798,0.500320275210389
9+: 985,0.500948416381545
10+:1181,0.500931161054265
Last edited by: 7craps on Mar 30, 2019
winsome johnny (not Win some johnny)
March 30th, 2019 at 7:11:12 AM
permalink
I did use it for a single Die and it broke down. So I moved over to a Markov chain solution to get an answer close to my simulation and have not returned to it until I saw this thread and your post here.Quote: Ace2Just curious...then why didn’t you use it before I did? I’d never seen it before yesterday, never had a need for that formula.
The pdf had no answers why it broke down.
This page shows more for the (-x)! problem and makes sense.
https://math.stackexchange.com/questions/1544460/group-of-r-people-at-least-three-people-have-the-same-birthday?noredirect=1&lq=1
where we take 1/n!=0 for n<0 (must have been added later)
again, lots of possible solutions
which are accurate all the time and which are not
winsome johnny (not Win some johnny)
April 4th, 2019 at 1:27:06 AM
permalink
Here are my results for the probability of four people having a common birthday by number in the group. I stopped the program when the probability of no common birthday to four people was less than 1 in a million.
The smallest number needed to have a greater than 50% chance is 187, with a 50.3% chance.
* Probability no four people in the group share the same birthday
The smallest number needed to have a greater than 50% chance is 187, with a 50.3% chance.
| People | Probability* |
|---|---|
| 4 | 0.0000000206 |
| 5 | 0.0000001026 |
| 6 | 0.0000003071 |
| 7 | 0.0000007150 |
| 8 | 0.0000014269 |
| 9 | 0.0000025629 |
| 10 | 0.0000042621 |
| 11 | 0.0000066829 |
| 12 | 0.0000100024 |
| 13 | 0.0000144163 |
| 14 | 0.0000201386 |
| 15 | 0.0000274016 |
| 16 | 0.0000364554 |
| 17 | 0.0000475679 |
| 18 | 0.0000610247 |
| 19 | 0.0000771284 |
| 20 | 0.0000961991 |
| 21 | 0.0001185734 |
| 22 | 0.0001446050 |
| 23 | 0.0001746637 |
| 24 | 0.0002091358 |
| 25 | 0.0002484237 |
| 26 | 0.0002929456 |
| 27 | 0.0003431352 |
| 28 | 0.0003994419 |
| 29 | 0.0004623302 |
| 30 | 0.0005322795 |
| 31 | 0.0006097840 |
| 32 | 0.0006953527 |
| 33 | 0.0007895086 |
| 34 | 0.0008927891 |
| 35 | 0.0010057453 |
| 36 | 0.0011289420 |
| 37 | 0.0012629575 |
| 38 | 0.0014083831 |
| 39 | 0.0015658233 |
| 40 | 0.0017358951 |
| 41 | 0.0019192279 |
| 42 | 0.0021164635 |
| 43 | 0.0023282555 |
| 44 | 0.0025552691 |
| 45 | 0.0027981811 |
| 46 | 0.0030576791 |
| 47 | 0.0033344619 |
| 48 | 0.0036292385 |
| 49 | 0.0039427286 |
| 50 | 0.0042756614 |
| 51 | 0.0046287760 |
| 52 | 0.0050028209 |
| 53 | 0.0053985534 |
| 54 | 0.0058167396 |
| 55 | 0.0062581541 |
| 56 | 0.0067235794 |
| 57 | 0.0072138055 |
| 58 | 0.0077296301 |
| 59 | 0.0082718575 |
| 60 | 0.0088412987 |
| 61 | 0.0094387710 |
| 62 | 0.0100650972 |
| 63 | 0.0107211059 |
| 64 | 0.0114076303 |
| 65 | 0.0121255084 |
| 66 | 0.0128755823 |
| 67 | 0.0136586978 |
| 68 | 0.0144757039 |
| 69 | 0.0153274525 |
| 70 | 0.0162147979 |
| 71 | 0.0171385959 |
| 72 | 0.0180997042 |
| 73 | 0.0190989810 |
| 74 | 0.0201372851 |
| 75 | 0.0212154750 |
| 76 | 0.0223344087 |
| 77 | 0.0234949430 |
| 78 | 0.0246979329 |
| 79 | 0.0259442312 |
| 80 | 0.0272346878 |
| 81 | 0.0285701492 |
| 82 | 0.0299514581 |
| 83 | 0.0313794524 |
| 84 | 0.0328549649 |
| 85 | 0.0343788228 |
| 86 | 0.0359518467 |
| 87 | 0.0375748502 |
| 88 | 0.0392486396 |
| 89 | 0.0409740125 |
| 90 | 0.0427517578 |
| 91 | 0.0445826550 |
| 92 | 0.0464674731 |
| 93 | 0.0484069703 |
| 94 | 0.0504018934 |
| 95 | 0.0524529768 |
| 96 | 0.0545609421 |
| 97 | 0.0567264973 |
| 98 | 0.0589503360 |
| 99 | 0.0612331369 |
| 100 | 0.0635755632 |
| 101 | 0.0659782614 |
| 102 | 0.0684418612 |
| 103 | 0.0709669743 |
| 104 | 0.0735541942 |
| 105 | 0.0762040949 |
| 106 | 0.0789172307 |
| 107 | 0.0816941352 |
| 108 | 0.0845353208 |
| 109 | 0.0874412778 |
| 110 | 0.0904124739 |
| 111 | 0.0934493532 |
| 112 | 0.0965523358 |
| 113 | 0.0997218173 |
| 114 | 0.1029581674 |
| 115 | 0.1062617299 |
| 116 | 0.1096328218 |
| 117 | 0.1130717325 |
| 118 | 0.1165787236 |
| 119 | 0.1201540276 |
| 120 | 0.1237978478 |
| 121 | 0.1275103576 |
| 122 | 0.1312916996 |
| 123 | 0.1351419854 |
| 124 | 0.1390612947 |
| 125 | 0.1430496749 |
| 126 | 0.1471071407 |
| 127 | 0.1512336731 |
| 128 | 0.1554292195 |
| 129 | 0.1596936927 |
| 130 | 0.1640269708 |
| 131 | 0.1684288964 |
| 132 | 0.1728992766 |
| 133 | 0.1774378821 |
| 134 | 0.1820444473 |
| 135 | 0.1867186694 |
| 136 | 0.1914602088 |
| 137 | 0.1962686881 |
| 138 | 0.2011436922 |
| 139 | 0.2060847678 |
| 140 | 0.2110914236 |
| 141 | 0.2161631296 |
| 142 | 0.2212993174 |
| 143 | 0.2264993796 |
| 144 | 0.2317626702 |
| 145 | 0.2370885041 |
| 146 | 0.2424761574 |
| 147 | 0.2479248672 |
| 148 | 0.2534338318 |
| 149 | 0.2590022105 |
| 150 | 0.2646291240 |
| 151 | 0.2703136545 |
| 152 | 0.2760548457 |
| 153 | 0.2818517033 |
| 154 | 0.2877031949 |
| 155 | 0.2936082507 |
| 156 | 0.2995657636 |
| 157 | 0.3055745896 |
| 158 | 0.3116335482 |
| 159 | 0.3177414229 |
| 160 | 0.3238969617 |
| 161 | 0.3300988777 |
| 162 | 0.3363458496 |
| 163 | 0.3426365222 |
| 164 | 0.3489695073 |
| 165 | 0.3553433841 |
| 166 | 0.3617567003 |
| 167 | 0.3682079725 |
| 168 | 0.3746956872 |
| 169 | 0.3812183018 |
| 170 | 0.3877742451 |
| 171 | 0.3943619186 |
| 172 | 0.4009796972 |
| 173 | 0.4076259303 |
| 174 | 0.4142989430 |
| 175 | 0.4209970368 |
| 176 | 0.4277184909 |
| 177 | 0.4344615634 |
| 178 | 0.4412244925 |
| 179 | 0.4480054975 |
| 180 | 0.4548027800 |
| 181 | 0.4616145254 |
| 182 | 0.4684389041 |
| 183 | 0.4752740728 |
| 184 | 0.4821181755 |
| 185 | 0.4889693456 |
| 186 | 0.4958257064 |
| 187 | 0.5026853732 |
| 188 | 0.5095464544 |
| 189 | 0.5164070529 |
| 190 | 0.5232652677 |
| 191 | 0.5301191954 |
| 192 | 0.5369669313 |
| 193 | 0.5438065713 |
| 194 | 0.5506362135 |
| 195 | 0.5574539590 |
| 196 | 0.5642579142 |
| 197 | 0.5710461918 |
| 198 | 0.5778169126 |
| 199 | 0.5845682068 |
| 200 | 0.5912982156 |
| 201 | 0.5980050928 |
| 202 | 0.6046870061 |
| 203 | 0.6113421387 |
| 204 | 0.6179686908 |
| 205 | 0.6245648809 |
| 206 | 0.6311289474 |
| 207 | 0.6376591501 |
| 208 | 0.6441537714 |
| 209 | 0.6506111178 |
| 210 | 0.6570295212 |
| 211 | 0.6634073405 |
| 212 | 0.6697429625 |
| 213 | 0.6760348034 |
| 214 | 0.6822813101 |
| 215 | 0.6884809614 |
| 216 | 0.6946322692 |
| 217 | 0.7007337794 |
| 218 | 0.7067840735 |
| 219 | 0.7127817691 |
| 220 | 0.7187255215 |
| 221 | 0.7246140243 |
| 222 | 0.7304460103 |
| 223 | 0.7362202530 |
| 224 | 0.7419355665 |
| 225 | 0.7475908073 |
| 226 | 0.7531848742 |
| 227 | 0.7587167097 |
| 228 | 0.7641853002 |
| 229 | 0.7695896769 |
| 230 | 0.7749289160 |
| 231 | 0.7802021396 |
| 232 | 0.7854085160 |
| 233 | 0.7905472598 |
| 234 | 0.7956176327 |
| 235 | 0.8006189436 |
| 236 | 0.8055505486 |
| 237 | 0.8104118517 |
| 238 | 0.8152023042 |
| 239 | 0.8199214054 |
| 240 | 0.8245687023 |
| 241 | 0.8291437895 |
| 242 | 0.8336463092 |
| 243 | 0.8380759511 |
| 244 | 0.8424324521 |
| 245 | 0.8467155959 |
| 246 | 0.8509252129 |
| 247 | 0.8550611798 |
| 248 | 0.8591234190 |
| 249 | 0.8631118982 |
| 250 | 0.8670266300 |
| 251 | 0.8708676712 |
| 252 | 0.8746351222 |
| 253 | 0.8783291262 |
| 254 | 0.8819498689 |
| 255 | 0.8854975772 |
| 256 | 0.8889725189 |
| 257 | 0.8923750015 |
| 258 | 0.8957053716 |
| 259 | 0.8989640138 |
| 260 | 0.9021513497 |
| 261 | 0.9052678373 |
| 262 | 0.9083139695 |
| 263 | 0.9112902735 |
| 264 | 0.9141973095 |
| 265 | 0.9170356696 |
| 266 | 0.9198059767 |
| 267 | 0.9225088837 |
| 268 | 0.9251450717 |
| 269 | 0.9277152494 |
| 270 | 0.9302201519 |
| 271 | 0.9326605389 |
| 272 | 0.9350371943 |
| 273 | 0.9373509246 |
| 274 | 0.9396025573 |
| 275 | 0.9417929406 |
| 276 | 0.9439229414 |
| 277 | 0.9459934441 |
| 278 | 0.9480053499 |
| 279 | 0.9499595753 |
| 280 | 0.9518570505 |
| 281 | 0.9536987190 |
| 282 | 0.9554855354 |
| 283 | 0.9572184653 |
| 284 | 0.9588984832 |
| 285 | 0.9605265717 |
| 286 | 0.9621037206 |
| 287 | 0.9636309253 |
| 288 | 0.9651091860 |
| 289 | 0.9665395064 |
| 290 | 0.9679228930 |
| 291 | 0.9692603534 |
| 292 | 0.9705528961 |
| 293 | 0.9718015286 |
| 294 | 0.9730072573 |
| 295 | 0.9741710859 |
| 296 | 0.9752940147 |
| 297 | 0.9763770399 |
| 298 | 0.9774211525 |
| 299 | 0.9784273375 |
| 300 | 0.9793965730 |
| 301 | 0.9803298300 |
| 302 | 0.9812280707 |
| 303 | 0.9820922487 |
| 304 | 0.9829233078 |
| 305 | 0.9837221815 |
| 306 | 0.9844897926 |
| 307 | 0.9852270522 |
| 308 | 0.9859348595 |
| 309 | 0.9866141012 |
| 310 | 0.9872656511 |
| 311 | 0.9878903695 |
| 312 | 0.9884891028 |
| 313 | 0.9890626833 |
| 314 | 0.9896119288 |
| 315 | 0.9901376421 |
| 316 | 0.9906406110 |
| 317 | 0.9911216078 |
| 318 | 0.9915813893 |
| 319 | 0.9920206964 |
| 320 | 0.9924402542 |
| 321 | 0.9928407714 |
| 322 | 0.9932229409 |
| 323 | 0.9935874390 |
| 324 | 0.9939349259 |
| 325 | 0.9942660452 |
| 326 | 0.9945814242 |
| 327 | 0.9948816741 |
| 328 | 0.9951673895 |
| 329 | 0.9954391488 |
| 330 | 0.9956975142 |
| 331 | 0.9959430321 |
| 332 | 0.9961762326 |
| 333 | 0.9963976302 |
| 334 | 0.9966077237 |
| 335 | 0.9968069963 |
| 336 | 0.9969959162 |
| 337 | 0.9971749362 |
| 338 | 0.9973444943 |
| 339 | 0.9975050139 |
| 340 | 0.9976569040 |
| 341 | 0.9978005591 |
| 342 | 0.9979363602 |
| 343 | 0.9980646744 |
| 344 | 0.9981858555 |
| 345 | 0.9983002440 |
| 346 | 0.9984081678 |
| 347 | 0.9985099421 |
| 348 | 0.9986058699 |
| 349 | 0.9986962422 |
| 350 | 0.9987813384 |
| 351 | 0.9988614264 |
| 352 | 0.9989367633 |
| 353 | 0.9990075953 |
| 354 | 0.9990741580 |
| 355 | 0.9991366772 |
| 356 | 0.9991953685 |
| 357 | 0.9992504383 |
| 358 | 0.9993020835 |
| 359 | 0.9993504921 |
| 360 | 0.9993958436 |
| 361 | 0.9994383091 |
| 362 | 0.9994780515 |
| 363 | 0.9995152260 |
| 364 | 0.9995499803 |
| 365 | 0.9995824550 |
| 366 | 0.9996127836 |
| 367 | 0.9996410928 |
| 368 | 0.9996675032 |
| 369 | 0.9996921289 |
| 370 | 0.9997150782 |
| 371 | 0.9997364538 |
| 372 | 0.9997563529 |
| 373 | 0.9997748675 |
| 374 | 0.9997920845 |
| 375 | 0.9998080861 |
| 376 | 0.9998229501 |
| 377 | 0.9998367496 |
| 378 | 0.9998495540 |
| 379 | 0.9998614284 |
| 380 | 0.9998724342 |
| 381 | 0.9998826293 |
| 382 | 0.9998920682 |
| 383 | 0.9999008020 |
| 384 | 0.9999088788 |
| 385 | 0.9999163440 |
| 386 | 0.9999232398 |
| 387 | 0.9999296061 |
| 388 | 0.9999354802 |
| 389 | 0.9999408971 |
| 390 | 0.9999458894 |
| 391 | 0.9999504879 |
| 392 | 0.9999547210 |
| 393 | 0.9999586157 |
| 394 | 0.9999621968 |
| 395 | 0.9999654876 |
| 396 | 0.9999685101 |
| 397 | 0.9999712843 |
| 398 | 0.9999738291 |
| 399 | 0.9999761623 |
| 400 | 0.9999783000 |
| 401 | 0.9999802575 |
| 402 | 0.9999820490 |
| 403 | 0.9999836874 |
| 404 | 0.9999851851 |
| 405 | 0.9999865532 |
| 406 | 0.9999878021 |
| 407 | 0.9999889417 |
| 408 | 0.9999899808 |
| 409 | 0.9999909277 |
| 410 | 0.9999917901 |
| 411 | 0.9999925749 |
| 412 | 0.9999932888 |
| 413 | 0.9999939378 |
| 414 | 0.9999945273 |
| 415 | 0.9999950626 |
| 416 | 0.9999955482 |
| 417 | 0.9999959886 |
| 418 | 0.9999963876 |
| 419 | 0.9999967490 |
| 420 | 0.9999970760 |
| 421 | 0.9999973718 |
| 422 | 0.9999976391 |
| 423 | 0.9999978806 |
| 424 | 0.9999980986 |
| 425 | 0.9999982953 |
| 426 | 0.9999984726 |
| 427 | 0.9999986323 |
| 428 | 0.9999987761 |
| 429 | 0.9999989055 |
| 430 | 0.9999990218 |
* Probability no four people in the group share the same birthday
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
April 4th, 2019 at 6:07:52 AM
permalink
Here are the results for the probability of five people sharing a common birthday. The median is 313.
* Probability that five people or more share a common birthday
| People | Probability* |
|---|---|
| 5 | 0.0000000001 |
| 7 | 0.0000000012 |
| 8 | 0.0000000031 |
| 9 | 0.0000000070 |
| 10 | 0.0000000140 |
| 11 | 0.0000000257 |
| 12 | 0.0000000439 |
| 13 | 0.0000000712 |
| 14 | 0.0000001105 |
| 15 | 0.0000001654 |
| 16 | 0.0000002400 |
| 17 | 0.0000003392 |
| 18 | 0.0000004686 |
| 19 | 0.0000006345 |
| 20 | 0.0000008441 |
| 21 | 0.0000011053 |
| 22 | 0.0000014272 |
| 23 | 0.0000018195 |
| 24 | 0.0000022930 |
| 25 | 0.0000028597 |
| 26 | 0.0000035326 |
| 27 | 0.0000043255 |
| 28 | 0.0000052539 |
| 29 | 0.0000063339 |
| 30 | 0.0000075834 |
| 31 | 0.0000090211 |
| 32 | 0.0000106673 |
| 33 | 0.0000125436 |
| 34 | 0.0000146727 |
| 35 | 0.0000170792 |
| 36 | 0.0000197887 |
| 37 | 0.0000228285 |
| 38 | 0.0000262274 |
| 39 | 0.0000300158 |
| 40 | 0.0000342256 |
| 41 | 0.0000388903 |
| 42 | 0.0000440452 |
| 43 | 0.0000497270 |
| 44 | 0.0000559744 |
| 45 | 0.0000628276 |
| 46 | 0.0000703289 |
| 47 | 0.0000785219 |
| 48 | 0.0000874526 |
| 49 | 0.0000971683 |
| 50 | 0.0001077187 |
| 51 | 0.0001191549 |
| 52 | 0.0001315304 |
| 53 | 0.0001449002 |
| 54 | 0.0001593218 |
| 55 | 0.0001748542 |
| 56 | 0.0001915588 |
| 57 | 0.0002094988 |
| 58 | 0.0002287396 |
| 59 | 0.0002493488 |
| 60 | 0.0002713960 |
| 61 | 0.0002949528 |
| 62 | 0.0003200932 |
| 63 | 0.0003468932 |
| 64 | 0.0003754312 |
| 65 | 0.0004057877 |
| 66 | 0.0004380454 |
| 67 | 0.0004722892 |
| 68 | 0.0005086066 |
| 69 | 0.0005470869 |
| 70 | 0.0005878221 |
| 71 | 0.0006309063 |
| 72 | 0.0006764360 |
| 73 | 0.0007245101 |
| 74 | 0.0007752298 |
| 75 | 0.0008286987 |
| 76 | 0.0008850227 |
| 77 | 0.0009443102 |
| 78 | 0.0010066720 |
| 79 | 0.0010722212 |
| 80 | 0.0011410735 |
| 81 | 0.0012133469 |
| 82 | 0.0012891619 |
| 83 | 0.0013686415 |
| 84 | 0.0014519111 |
| 85 | 0.0015390986 |
| 86 | 0.0016303342 |
| 87 | 0.0017257510 |
| 88 | 0.0018254840 |
| 89 | 0.0019296713 |
| 90 | 0.0020384530 |
| 91 | 0.0021519719 |
| 92 | 0.0022703734 |
| 93 | 0.0023938051 |
| 94 | 0.0025224174 |
| 95 | 0.0026563631 |
| 96 | 0.0027957973 |
| 97 | 0.0029408778 |
| 98 | 0.0030917650 |
| 99 | 0.0032486214 |
| 100 | 0.0034116124 |
| 101 | 0.0035809056 |
| 102 | 0.0037566712 |
| 103 | 0.0039390818 |
| 104 | 0.0041283125 |
| 105 | 0.0043245408 |
| 106 | 0.0045279467 |
| 107 | 0.0047387126 |
| 108 | 0.0049570234 |
| 109 | 0.0051830661 |
| 110 | 0.0054170306 |
| 111 | 0.0056591088 |
| 112 | 0.0059094950 |
| 113 | 0.0061683860 |
| 114 | 0.0064359809 |
| 115 | 0.0067124810 |
| 116 | 0.0069980899 |
| 117 | 0.0072930137 |
| 118 | 0.0075974606 |
| 119 | 0.0079116409 |
| 120 | 0.0082357674 |
| 121 | 0.0085700549 |
| 122 | 0.0089147205 |
| 123 | 0.0092699832 |
| 124 | 0.0096360643 |
| 125 | 0.0100131873 |
| 126 | 0.0104015775 |
| 127 | 0.0108014623 |
| 128 | 0.0112130713 |
| 129 | 0.0116366357 |
| 130 | 0.0120723889 |
| 131 | 0.0125205661 |
| 132 | 0.0129814044 |
| 133 | 0.0134551427 |
| 134 | 0.0139420216 |
| 135 | 0.0144422836 |
| 136 | 0.0149561727 |
| 137 | 0.0154839347 |
| 138 | 0.0160258171 |
| 139 | 0.0165820686 |
| 140 | 0.0171529399 |
| 141 | 0.0177386829 |
| 142 | 0.0183395508 |
| 143 | 0.0189557985 |
| 144 | 0.0195876820 |
| 145 | 0.0202354587 |
| 146 | 0.0208993870 |
| 147 | 0.0215797267 |
| 148 | 0.0222767386 |
| 149 | 0.0229906846 |
| 150 | 0.0237218274 |
| 151 | 0.0244704307 |
| 152 | 0.0252367593 |
| 153 | 0.0260210785 |
| 154 | 0.0268236544 |
| 155 | 0.0276447538 |
| 156 | 0.0284846441 |
| 157 | 0.0293435931 |
| 158 | 0.0302218692 |
| 159 | 0.0311197411 |
| 160 | 0.0320374778 |
| 161 | 0.0329753486 |
| 162 | 0.0339336228 |
| 163 | 0.0349125698 |
| 164 | 0.0359124592 |
| 165 | 0.0369335602 |
| 166 | 0.0379761419 |
| 167 | 0.0390404734 |
| 168 | 0.0401268230 |
| 169 | 0.0412354589 |
| 170 | 0.0423666487 |
| 171 | 0.0435206592 |
| 172 | 0.0446977568 |
| 173 | 0.0458982068 |
| 174 | 0.0471222737 |
| 175 | 0.0483702211 |
| 176 | 0.0496423113 |
| 177 | 0.0509388056 |
| 178 | 0.0522599640 |
| 179 | 0.0536060448 |
| 180 | 0.0549773052 |
| 181 | 0.0563740004 |
| 182 | 0.0577963843 |
| 183 | 0.0592447086 |
| 184 | 0.0607192233 |
| 185 | 0.0622201763 |
| 186 | 0.0637478133 |
| 187 | 0.0653023777 |
| 188 | 0.0668841106 |
| 189 | 0.0684932506 |
| 190 | 0.0701300336 |
| 191 | 0.0717946930 |
| 192 | 0.0734874591 |
| 193 | 0.0752085593 |
| 194 | 0.0769582180 |
| 195 | 0.0787366562 |
| 196 | 0.0805440919 |
| 197 | 0.0823807393 |
| 198 | 0.0842468093 |
| 199 | 0.0861425089 |
| 200 | 0.0880680413 |
| 201 | 0.0900236059 |
| 202 | 0.0920093979 |
| 203 | 0.0940256083 |
| 204 | 0.0960724238 |
| 205 | 0.0981500266 |
| 206 | 0.1002585944 |
| 207 | 0.1023983001 |
| 208 | 0.1045693119 |
| 209 | 0.1067717927 |
| 210 | 0.1090059007 |
| 211 | 0.1112717886 |
| 212 | 0.1135696037 |
| 213 | 0.1158994881 |
| 214 | 0.1182615781 |
| 215 | 0.1206560041 |
| 216 | 0.1230828909 |
| 217 | 0.1255423571 |
| 218 | 0.1280345153 |
| 219 | 0.1305594717 |
| 220 | 0.1331173263 |
| 221 | 0.1357081722 |
| 222 | 0.1383320964 |
| 223 | 0.1409891786 |
| 224 | 0.1436794920 |
| 225 | 0.1464031026 |
| 226 | 0.1491600693 |
| 227 | 0.1519504437 |
| 228 | 0.1547742701 |
| 229 | 0.1576315852 |
| 230 | 0.1605224181 |
| 231 | 0.1634467903 |
| 232 | 0.1664047154 |
| 233 | 0.1693961988 |
| 234 | 0.1724212381 |
| 235 | 0.1754798228 |
| 236 | 0.1785719337 |
| 237 | 0.1816975436 |
| 238 | 0.1848566167 |
| 239 | 0.1880491084 |
| 240 | 0.1912749658 |
| 241 | 0.1945341267 |
| 242 | 0.1978265206 |
| 243 | 0.2011520675 |
| 244 | 0.2045106786 |
| 245 | 0.2079022559 |
| 246 | 0.2113266923 |
| 247 | 0.2147838710 |
| 248 | 0.2182736663 |
| 249 | 0.2217959427 |
| 250 | 0.2253505553 |
| 251 | 0.2289373496 |
| 252 | 0.2325561615 |
| 253 | 0.2362068169 |
| 254 | 0.2398891322 |
| 255 | 0.2436029141 |
| 256 | 0.2473479589 |
| 257 | 0.2511240536 |
| 258 | 0.2549309748 |
| 259 | 0.2587684893 |
| 260 | 0.2626363538 |
| 261 | 0.2665343151 |
| 262 | 0.2704621097 |
| 263 | 0.2744194642 |
| 264 | 0.2784060950 |
| 265 | 0.2824217084 |
| 266 | 0.2864660006 |
| 267 | 0.2905386578 |
| 268 | 0.2946393558 |
| 269 | 0.2987677605 |
| 270 | 0.3029235279 |
| 271 | 0.3071063035 |
| 272 | 0.3113157232 |
| 273 | 0.3155514127 |
| 274 | 0.3198129877 |
| 275 | 0.3241000540 |
| 276 | 0.3284122077 |
| 277 | 0.3327490349 |
| 278 | 0.3371101120 |
| 279 | 0.3414950058 |
| 280 | 0.3459032733 |
| 281 | 0.3503344621 |
| 282 | 0.3547881103 |
| 283 | 0.3592637466 |
| 284 | 0.3637608905 |
| 285 | 0.3682790523 |
| 286 | 0.3728177332 |
| 287 | 0.3773764254 |
| 288 | 0.3819546123 |
| 289 | 0.3865517687 |
| 290 | 0.3911673607 |
| 291 | 0.3958008458 |
| 292 | 0.4004516735 |
| 293 | 0.4051192850 |
| 294 | 0.4098031133 |
| 295 | 0.4145025838 |
| 296 | 0.4192171142 |
| 297 | 0.4239461145 |
| 298 | 0.4286889875 |
| 299 | 0.4334451288 |
| 300 | 0.4382139270 |
| 301 | 0.4429947640 |
| 302 | 0.4477870151 |
| 303 | 0.4525900490 |
| 304 | 0.4574032286 |
| 305 | 0.4622259106 |
| 306 | 0.4670574460 |
| 307 | 0.4718971803 |
| 308 | 0.4767444538 |
| 309 | 0.4815986015 |
| 310 | 0.4864589539 |
| 311 | 0.4913248368 |
| 312 | 0.4961955716 |
| 313 | 0.5010704758 |
| 314 | 0.5059488630 |
| 315 | 0.5108300433 |
| 316 | 0.5157133233 |
| 317 | 0.5205980070 |
| 318 | 0.5254833953 |
| 319 | 0.5303687869 |
| 320 | 0.5352534780 |
| 321 | 0.5401367634 |
| 322 | 0.5450179357 |
| 323 | 0.5498962867 |
| 324 | 0.5547711068 |
| 325 | 0.5596416859 |
| 326 | 0.5645073134 |
| 327 | 0.5693672786 |
| 328 | 0.5742208707 |
| 329 | 0.5790673799 |
| 330 | 0.5839060966 |
| 331 | 0.5887363127 |
| 332 | 0.5935573214 |
| 333 | 0.5983684174 |
| 334 | 0.6031688977 |
| 335 | 0.6079580613 |
| 336 | 0.6127352102 |
| 337 | 0.6174996491 |
| 338 | 0.6222506860 |
| 339 | 0.6269876324 |
| 340 | 0.6317098038 |
| 341 | 0.6364165199 |
| 342 | 0.6411071047 |
| 343 | 0.6457808872 |
| 344 | 0.6504372014 |
| 345 | 0.6550753866 |
| 346 | 0.6596947881 |
| 347 | 0.6642947570 |
| 348 | 0.6688746506 |
| 349 | 0.6734338331 |
| 350 | 0.6779716753 |
| 351 | 0.6824875554 |
| 352 | 0.6869808588 |
| 353 | 0.6914509790 |
| 354 | 0.6958973171 |
| 355 | 0.7003192829 |
| 356 | 0.7047162944 |
| 357 | 0.7090877787 |
| 358 | 0.7134331719 |
| 359 | 0.7177519192 |
| 360 | 0.7220434758 |
| 361 | 0.7263073064 |
| 362 | 0.7305428860 |
| 363 | 0.7347496997 |
| 364 | 0.7389272432 |
| 365 | 0.7430750229 |
| 366 | 0.7471925564 |
| 367 | 0.7512793721 |
| 368 | 0.7553350101 |
| 369 | 0.7593590217 |
| 370 | 0.7633509703 |
| 371 | 0.7673104310 |
| 372 | 0.7712369910 |
| 373 | 0.7751302499 |
| 374 | 0.7789898196 |
| 375 | 0.7828153245 |
| 376 | 0.7866064018 |
| 377 | 0.7903627015 |
| 378 | 0.7940838866 |
| 379 | 0.7977696331 |
| 380 | 0.8014196301 |
| 381 | 0.8050335802 |
| 382 | 0.8086111990 |
| 383 | 0.8121522160 |
| 384 | 0.8156563738 |
| 385 | 0.8191234288 |
| 386 | 0.8225531508 |
| 387 | 0.8259453237 |
| 388 | 0.8292997446 |
| 389 | 0.8326162246 |
| 390 | 0.8358945885 |
| 391 | 0.8391346750 |
| 392 | 0.8423363362 |
| 393 | 0.8454994383 |
| 394 | 0.8486238611 |
| 395 | 0.8517094980 |
| 396 | 0.8547562563 |
| 397 | 0.8577640565 |
| 398 | 0.8607328332 |
| 399 | 0.8636625340 |
| 400 | 0.8665531203 |
| 401 | 0.8694045666 |
| 402 | 0.8722168609 |
| 403 | 0.8749900040 |
| 404 | 0.8777240101 |
| 405 | 0.8804189062 |
| 406 | 0.8830747321 |
| 407 | 0.8856915403 |
| 408 | 0.8882693959 |
| 409 | 0.8908083763 |
| 410 | 0.8933085712 |
| 411 | 0.8957700826 |
| 412 | 0.8981930239 |
| 413 | 0.9005775209 |
| 414 | 0.9029237105 |
| 415 | 0.9052317411 |
| 416 | 0.9075017724 |
| 417 | 0.9097339751 |
| 418 | 0.9119285304 |
| 419 | 0.9140856304 |
| 420 | 0.9162054773 |
| 421 | 0.9182882837 |
| 422 | 0.9203342720 |
| 423 | 0.9223436740 |
| 424 | 0.9243167314 |
| 425 | 0.9262536948 |
| 426 | 0.9281548238 |
| 427 | 0.9300203867 |
| 428 | 0.9318506603 |
| 429 | 0.9336459296 |
| 430 | 0.9354064875 |
| 431 | 0.9371326346 |
| 432 | 0.9388246788 |
| 433 | 0.9404829353 |
| 434 | 0.9421077261 |
| 435 | 0.9436993798 |
| 436 | 0.9452582315 |
| 437 | 0.9467846220 |
| 438 | 0.9482788983 |
| 439 | 0.9497414126 |
| 440 | 0.9511725226 |
| 441 | 0.9525725907 |
| 442 | 0.9539419842 |
| 443 | 0.9552810748 |
| 444 | 0.9565902382 |
| 445 | 0.9578698541 |
| 446 | 0.9591203057 |
| 447 | 0.9603419797 |
| 448 | 0.9615352657 |
| 449 | 0.9627005562 |
| 450 | 0.9638382461 |
| 451 | 0.9649487327 |
| 452 | 0.9660324152 |
| 453 | 0.9670896946 |
| 454 | 0.9681209735 |
| 455 | 0.9691266554 |
| 456 | 0.9701071453 |
| 457 | 0.9710628485 |
| 458 | 0.9719941710 |
| 459 | 0.9729015191 |
| 460 | 0.9737852990 |
| 461 | 0.9746459169 |
| 462 | 0.9754837784 |
| 463 | 0.9762992884 |
| 464 | 0.9770928513 |
| 465 | 0.9778648701 |
| 466 | 0.9786157466 |
| 467 | 0.9793458812 |
| 468 | 0.9800556725 |
| 469 | 0.9807455174 |
| 470 | 0.9814158107 |
| 471 | 0.9820669448 |
| 472 | 0.9826993099 |
| 473 | 0.9833132935 |
| 474 | 0.9839092804 |
| 475 | 0.9844876526 |
| 476 | 0.9850487889 |
| 477 | 0.9855930650 |
| 478 | 0.9861208531 |
| 479 | 0.9866325221 |
| 480 | 0.9871284372 |
| 481 | 0.9876089599 |
| 482 | 0.9880744478 |
| 483 | 0.9885252547 |
| 484 | 0.9889617301 |
| 485 | 0.9893842194 |
| 486 | 0.9897930639 |
| 487 | 0.9901886003 |
| 488 | 0.9905711610 |
| 489 | 0.9909410738 |
| 490 | 0.9912986620 |
| 491 | 0.9916442443 |
| 492 | 0.9919781344 |
| 493 | 0.9923006414 |
| 494 | 0.9926120697 |
| 495 | 0.9929127187 |
| 496 | 0.9932028827 |
| 497 | 0.9934828514 |
| 498 | 0.9937529092 |
| 499 | 0.9940133358 |
| 500 | 0.9942644056 |
| 501 | 0.9945063881 |
| 502 | 0.9947395476 |
| 503 | 0.9949641437 |
| 504 | 0.9951804304 |
| 505 | 0.9953886570 |
| 506 | 0.9955890678 |
| 507 | 0.9957819017 |
| 508 | 0.9959673929 |
| 509 | 0.9961457704 |
| 510 | 0.9963172583 |
| 511 | 0.9964820756 |
| 512 | 0.9966404365 |
| 513 | 0.9967925502 |
| 514 | 0.9969386211 |
| 515 | 0.9970788486 |
| 516 | 0.9972134275 |
| 517 | 0.9973425476 |
| 518 | 0.9974663943 |
| 519 | 0.9975851481 |
| 520 | 0.9976989850 |
| 521 | 0.9978080762 |
| 522 | 0.9979125888 |
| 523 | 0.9980126851 |
| 524 | 0.9981085232 |
| 525 | 0.9982002568 |
| 526 | 0.9982880354 |
| 527 | 0.9983720041 |
| 528 | 0.9984523041 |
| 529 | 0.9985290723 |
| 530 | 0.9986024419 |
| 531 | 0.9986725418 |
| 532 | 0.9987394973 |
| 533 | 0.9988034298 |
| 534 | 0.9988644569 |
| 535 | 0.9989226927 |
| 536 | 0.9989782476 |
| 537 | 0.9990312286 |
| 538 | 0.9990817391 |
| 539 | 0.9991298792 |
| 540 | 0.9991757457 |
| 541 | 0.9992194323 |
| 542 | 0.9992610293 |
| 543 | 0.9993006242 |
| 544 | 0.9993383014 |
| 545 | 0.9993741421 |
| 546 | 0.9994082251 |
| 547 | 0.9994406260 |
| 548 | 0.9994714181 |
| 549 | 0.9995006716 |
| 550 | 0.9995284544 |
| 551 | 0.9995548320 |
| 552 | 0.9995798671 |
| 553 | 0.9996036202 |
| 554 | 0.9996261497 |
| 555 | 0.9996475115 |
| 556 | 0.9996677595 |
| 557 | 0.9996869452 |
| 558 | 0.9997051184 |
| 559 | 0.9997223268 |
| 560 | 0.9997386161 |
| 561 | 0.9997540302 |
| 562 | 0.9997686112 |
| 563 | 0.9997823995 |
| 564 | 0.9997954337 |
| 565 | 0.9998077509 |
| 566 | 0.9998193865 |
| 567 | 0.9998303745 |
| 568 | 0.9998407474 |
| 569 | 0.9998505361 |
| 570 | 0.9998597705 |
| 571 | 0.9998684788 |
| 572 | 0.9998766882 |
| 573 | 0.9998844245 |
| 574 | 0.9998917125 |
| 575 | 0.9998985757 |
| 576 | 0.9999050366 |
| 577 | 0.9999111166 |
| 578 | 0.9999168361 |
| 579 | 0.9999222147 |
| 580 | 0.9999272707 |
| 581 | 0.9999320220 |
| 582 | 0.9999364851 |
| 583 | 0.9999406761 |
| 584 | 0.9999446101 |
| 585 | 0.9999483016 |
| 586 | 0.9999517642 |
| 587 | 0.9999550110 |
| 588 | 0.9999580543 |
| 589 | 0.9999609057 |
| 590 | 0.9999635765 |
| 591 | 0.9999660770 |
| 592 | 0.9999684174 |
| 593 | 0.9999706070 |
| 594 | 0.9999726548 |
| 595 | 0.9999745693 |
| 596 | 0.9999763584 |
| 597 | 0.9999780297 |
| 598 | 0.9999795905 |
| 599 | 0.9999810474 |
| 600 | 0.9999824069 |
| 601 | 0.9999836750 |
| 602 | 0.9999848573 |
| 603 | 0.9999859593 |
| 604 | 0.9999869860 |
| 605 | 0.9999879422 |
| 606 | 0.9999888324 |
| 607 | 0.9999896608 |
| 608 | 0.9999904315 |
| 609 | 0.9999911480 |
| 610 | 0.9999918141 |
| 611 | 0.9999924330 |
| 612 | 0.9999930078 |
| 613 | 0.9999935414 |
| 614 | 0.9999940367 |
| 615 | 0.9999944961 |
| 616 | 0.9999949221 |
| 617 | 0.9999953170 |
| 618 | 0.9999956829 |
| 619 | 0.9999960218 |
| 620 | 0.9999963355 |
| 621 | 0.9999966258 |
| 622 | 0.9999968944 |
| 623 | 0.9999971428 |
| 624 | 0.9999973723 |
| 625 | 0.9999975844 |
| 626 | 0.9999977802 |
| 627 | 0.9999979611 |
| 628 | 0.9999981279 |
| 629 | 0.9999982818 |
| 630 | 0.9999984237 |
| 631 | 0.9999985545 |
| 632 | 0.9999986749 |
| 633 | 0.9999987859 |
| 634 | 0.9999988880 |
| 635 | 0.9999989819 |
| 636 | 0.9999990683 |
* Probability that five people or more share a common birthday
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
April 4th, 2019 at 1:59:48 PM
permalink
Thought I would throw on the 'mean' for at least 2 to 10 matches for the BDay problem.Quote: 7crapsadded: for at least X number of matches for the BDay problem
2+: 23,0.507297234323982
3+: 88,0.511065110624736 (87,0.499454850631405)
4+: 187,0.502685373188966
5+: 313,0.501070475849204
6+: 460,0.50244941036937
7+: 623,0.502948948664566 (622,0.499795687887501)
8+: 798,0.500320275210389
9+: 985,0.500948416381545
10+:1181,0.500931161054265
one can compare it to the median values above.
(Good job of taking over a thread. Maybe Google can find it in the future)
This was done using some R code talked about earlier in the thread.
(not posted yet)
[1] For at least 2 matches, 24.6166: average number of people
[1] For at least 3 matches, 88.7389: average number of people
[1] For at least 4 matches, 187.052: average number of people
[1] For at least 5 matches, 311.449: average number of people
[1] For at least 6 matches, 456.016: average number of people
[1] For at least 7 matches, 616.617: average number of people
[1] For at least 8 matches, 790.3: average number of people
[1] For at least 9 matches, 974.894: average number of people
[1] For at least 10 matches, 1168.76: average number of people
winsome johnny (not Win some johnny)
April 6th, 2019 at 5:59:20 AM
permalink
7Craps, that is some good stuff. I'm impressed you could calculate this much so fast. I'll have to look over your previous posts more carefully. The following list for six people having a common birthday took days of computer time. I had to start going in groups of 10 people because it was going so slowly. We agree on the median probability at 460 people.
* Probability represents probability at least six people will share at least one common birthday.
| People | Probability* |
|---|---|
| 6 | 0.0000000000 |
| 7 | 0.0000000000 |
| 8 | 0.0000000000 |
| 9 | 0.0000000000 |
| 10 | 0.0000000000 |
| 11 | 0.0000000001 |
| 12 | 0.0000000001 |
| 13 | 0.0000000003 |
| 14 | 0.0000000005 |
| 15 | 0.0000000008 |
| 16 | 0.0000000012 |
| 17 | 0.0000000019 |
| 18 | 0.0000000028 |
| 19 | 0.0000000041 |
| 20 | 0.0000000058 |
| 21 | 0.0000000081 |
| 22 | 0.0000000111 |
| 23 | 0.0000000150 |
| 24 | 0.0000000199 |
| 25 | 0.0000000261 |
| 26 | 0.0000000339 |
| 27 | 0.0000000435 |
| 28 | 0.0000000552 |
| 29 | 0.0000000695 |
| 30 | 0.0000000866 |
| 31 | 0.0000001072 |
| 32 | 0.0000001316 |
| 33 | 0.0000001605 |
| 34 | 0.0000001944 |
| 35 | 0.0000002340 |
| 36 | 0.0000002802 |
| 37 | 0.0000003336 |
| 38 | 0.0000003953 |
| 39 | 0.0000004661 |
| 40 | 0.0000005470 |
| 41 | 0.0000006393 |
| 42 | 0.0000007441 |
| 43 | 0.0000008627 |
| 44 | 0.0000009966 |
| 45 | 0.0000011472 |
| 46 | 0.0000013162 |
| 47 | 0.0000015053 |
| 48 | 0.0000017163 |
| 49 | 0.0000019512 |
| 50 | 0.0000022121 |
| 51 | 0.0000025011 |
| 52 | 0.0000028208 |
| 53 | 0.0000031734 |
| 54 | 0.0000035617 |
| 55 | 0.0000039885 |
| 56 | 0.0000044566 |
| 57 | 0.0000049693 |
| 58 | 0.0000055296 |
| 59 | 0.0000061412 |
| 60 | 0.0000068076 |
| 61 | 0.0000075326 |
| 62 | 0.0000083201 |
| 63 | 0.0000091743 |
| 64 | 0.0000100997 |
| 65 | 0.0000111007 |
| 66 | 0.0000121822 |
| 67 | 0.0000133491 |
| 68 | 0.0000146067 |
| 69 | 0.0000159604 |
| 70 | 0.0000174158 |
| 71 | 0.0000189788 |
| 72 | 0.0000206557 |
| 73 | 0.0000224528 |
| 74 | 0.0000243767 |
| 75 | 0.0000264344 |
| 76 | 0.0000286330 |
| 77 | 0.0000309800 |
| 78 | 0.0000334831 |
| 79 | 0.0000361503 |
| 80 | 0.0000389900 |
| 81 | 0.0000420106 |
| 82 | 0.0000452211 |
| 83 | 0.0000486308 |
| 84 | 0.0000522490 |
| 85 | 0.0000560857 |
| 86 | 0.0000601510 |
| 87 | 0.0000644554 |
| 88 | 0.0000690098 |
| 89 | 0.0000738253 |
| 90 | 0.0000789134 |
| 91 | 0.0000842860 |
| 92 | 0.0000899554 |
| 93 | 0.0000959342 |
| 94 | 0.0001022353 |
| 95 | 0.0001088721 |
| 96 | 0.0001158585 |
| 97 | 0.0001232085 |
| 98 | 0.0001309366 |
| 99 | 0.0001390579 |
| 100 | 0.0001475877 |
| 101 | 0.0001565418 |
| 102 | 0.0001659363 |
| 103 | 0.0001757880 |
| 104 | 0.0001861138 |
| 105 | 0.0001969314 |
| 106 | 0.0002082586 |
| 107 | 0.0002201138 |
| 108 | 0.0002325161 |
| 109 | 0.0002454846 |
| 110 | 0.0002590392 |
| 111 | 0.0002732003 |
| 112 | 0.0002879885 |
| 113 | 0.0003034251 |
| 114 | 0.0003195320 |
| 115 | 0.0003363313 |
| 116 | 0.0003538459 |
| 117 | 0.0003720990 |
| 118 | 0.0003911145 |
| 119 | 0.0004109166 |
| 120 | 0.0004315303 |
| 121 | 0.0004529809 |
| 122 | 0.0004752945 |
| 123 | 0.0004984974 |
| 124 | 0.0005226168 |
| 125 | 0.0005476802 |
| 126 | 0.0005737159 |
| 127 | 0.0006007526 |
| 128 | 0.0006288195 |
| 129 | 0.0006579467 |
| 130 | 0.0006881647 |
| 131 | 0.0007195044 |
| 132 | 0.0007519977 |
| 133 | 0.0007856768 |
| 134 | 0.0008205746 |
| 135 | 0.0008567246 |
| 136 | 0.0008941611 |
| 137 | 0.0009329187 |
| 138 | 0.0009730328 |
| 139 | 0.0010145396 |
| 140 | 0.0010574756 |
| 141 | 0.0011018783 |
| 142 | 0.0011477855 |
| 143 | 0.0011952360 |
| 144 | 0.0012442689 |
| 145 | 0.0012949244 |
| 146 | 0.0013472429 |
| 147 | 0.0014012659 |
| 148 | 0.0014570352 |
| 149 | 0.0015145937 |
| 150 | 0.0015739845 |
| 151 | 0.0016352519 |
| 152 | 0.0016984405 |
| 153 | 0.0017635958 |
| 154 | 0.0018307639 |
| 155 | 0.0018999918 |
| 156 | 0.0019713270 |
| 157 | 0.0020448178 |
| 158 | 0.0021205132 |
| 159 | 0.0021984630 |
| 160 | 0.0022787177 |
| 161 | 0.0023613285 |
| 162 | 0.0024463474 |
| 163 | 0.0025338269 |
| 164 | 0.0026238207 |
| 165 | 0.0027163828 |
| 166 | 0.0028115682 |
| 167 | 0.0029094326 |
| 168 | 0.0030100324 |
| 169 | 0.0031134248 |
| 170 | 0.0032196678 |
| 171 | 0.0033288202 |
| 172 | 0.0034409414 |
| 173 | 0.0035560917 |
| 174 | 0.0036743321 |
| 175 | 0.0037957245 |
| 176 | 0.0039203315 |
| 177 | 0.0040482164 |
| 178 | 0.0041794433 |
| 179 | 0.0043140773 |
| 180 | 0.0044521840 |
| 181 | 0.0045938299 |
| 182 | 0.0047390824 |
| 183 | 0.0048880095 |
| 184 | 0.0050406801 |
| 185 | 0.0051971639 |
| 186 | 0.0053575313 |
| 187 | 0.0055218535 |
| 188 | 0.0056902027 |
| 189 | 0.0058626515 |
| 190 | 0.0060392738 |
| 191 | 0.0062201439 |
| 192 | 0.0064053369 |
| 193 | 0.0065949290 |
| 194 | 0.0067889969 |
| 195 | 0.0069876183 |
| 196 | 0.0071908715 |
| 197 | 0.0073988356 |
| 198 | 0.0076115908 |
| 199 | 0.0078292177 |
| 200 | 0.0080517980 |
| 201 | 0.0082794138 |
| 202 | 0.0085121485 |
| 203 | 0.0087500858 |
| 204 | 0.0089933106 |
| 205 | 0.0092419082 |
| 206 | 0.0094959649 |
| 207 | 0.0097555677 |
| 208 | 0.0100208045 |
| 209 | 0.0102917638 |
| 210 | 0.0105685349 |
| 211 | 0.0108512080 |
| 212 | 0.0111398739 |
| 213 | 0.0114346242 |
| 214 | 0.0117355512 |
| 215 | 0.0120427482 |
| 216 | 0.0123563089 |
| 217 | 0.0126763280 |
| 218 | 0.0130029008 |
| 219 | 0.0133361233 |
| 220 | 0.0136760922 |
| 221 | 0.0140229053 |
| 222 | 0.0143766605 |
| 223 | 0.0147374569 |
| 224 | 0.0151053940 |
| 225 | 0.0154805723 |
| 226 | 0.0158630926 |
| 227 | 0.0162530566 |
| 228 | 0.0166505668 |
| 229 | 0.0170557260 |
| 230 | 0.0174686381 |
| 231 | 0.0178894073 |
| 232 | 0.0183181386 |
| 233 | 0.0187549376 |
| 234 | 0.0191999105 |
| 235 | 0.0196531641 |
| 236 | 0.0201148060 |
| 237 | 0.0205849440 |
| 238 | 0.0210636870 |
| 239 | 0.0215511440 |
| 240 | 0.0220474248 |
| 241 | 0.0225526398 |
| 242 | 0.0230668998 |
| 243 | 0.0235903163 |
| 244 | 0.0241230011 |
| 245 | 0.0246650666 |
| 246 | 0.0252166259 |
| 247 | 0.0257777923 |
| 248 | 0.0263486798 |
| 249 | 0.0269294025 |
| 250 | 0.0275200754 |
| 251 | 0.0281208137 |
| 252 | 0.0287317329 |
| 253 | 0.0293529491 |
| 254 | 0.0299845789 |
| 255 | 0.0306267388 |
| 256 | 0.0312795462 |
| 257 | 0.0319431185 |
| 258 | 0.0326175735 |
| 259 | 0.0333030294 |
| 260 | 0.0339996046 |
| 261 | 0.0347074178 |
| 262 | 0.0354265880 |
| 263 | 0.0361572343 |
| 264 | 0.0368994762 |
| 265 | 0.0376534333 |
| 266 | 0.0384192254 |
| 267 | 0.0391969726 |
| 268 | 0.0399867949 |
| 269 | 0.0407888125 |
| 270 | 0.0416031460 |
| 271 | 0.0424299156 |
| 272 | 0.0432692420 |
| 273 | 0.0441212456 |
| 274 | 0.0449860471 |
| 275 | 0.0458637670 |
| 276 | 0.0467545259 |
| 277 | 0.0476584444 |
| 278 | 0.0485756428 |
| 279 | 0.0495062415 |
| 280 | 0.0504503609 |
| 281 | 0.0514081209 |
| 282 | 0.0523796415 |
| 283 | 0.0533650426 |
| 284 | 0.0543644436 |
| 285 | 0.0553779638 |
| 286 | 0.0564057224 |
| 287 | 0.0574478380 |
| 288 | 0.0585044291 |
| 289 | 0.0595756138 |
| 290 | 0.0606615099 |
| 291 | 0.0617622347 |
| 292 | 0.0628779050 |
| 293 | 0.0640086374 |
| 294 | 0.0651545478 |
| 295 | 0.0663157517 |
| 296 | 0.0674923640 |
| 297 | 0.0686844991 |
| 298 | 0.0698922707 |
| 299 | 0.0711157919 |
| 300 | 0.0723551752 |
| 301 | 0.0736105324 |
| 302 | 0.0748819746 |
| 303 | 0.0761696119 |
| 304 | 0.0774735540 |
| 305 | 0.0787939096 |
| 306 | 0.0801307864 |
| 307 | 0.0814842915 |
| 308 | 0.0828545309 |
| 309 | 0.0842416097 |
| 310 | 0.0856456320 |
| 311 | 0.0870667009 |
| 312 | 0.0885049184 |
| 313 | 0.0899603856 |
| 314 | 0.0914332023 |
| 315 | 0.0929234671 |
| 316 | 0.0944312775 |
| 317 | 0.0959567299 |
| 318 | 0.0974999192 |
| 319 | 0.0990609392 |
| 320 | 0.1006398823 |
| 321 | 0.1022368394 |
| 322 | 0.1038519001 |
| 323 | 0.1054851528 |
| 324 | 0.1071366840 |
| 325 | 0.1088065788 |
| 326 | 0.1104949211 |
| 327 | 0.1122017926 |
| 328 | 0.1139272740 |
| 329 | 0.1156714439 |
| 330 | 0.1174343793 |
| 331 | 0.1192161555 |
| 332 | 0.1210168461 |
| 333 | 0.1228365227 |
| 334 | 0.1246752552 |
| 335 | 0.1265331116 |
| 336 | 0.1284101577 |
| 337 | 0.1303064578 |
| 338 | 0.1322220738 |
| 339 | 0.1341570657 |
| 340 | 0.1361114914 |
| 341 | 0.1380854066 |
| 342 | 0.1400788651 |
| 343 | 0.1420919182 |
| 344 | 0.1441246150 |
| 345 | 0.1461770024 |
| 346 | 0.1482491251 |
| 347 | 0.1503410253 |
| 348 | 0.1524527427 |
| 349 | 0.1545843147 |
| 350 | 0.1567357764 |
| 351 | 0.1589071600 |
| 352 | 0.1610984955 |
| 353 | 0.1633098101 |
| 354 | 0.1655411285 |
| 355 | 0.1677924727 |
| 356 | 0.1700638621 |
| 357 | 0.1723553132 |
| 358 | 0.1746668398 |
| 359 | 0.1769984530 |
| 360 | 0.1793501608 |
| 361 | 0.1817219686 |
| 362 | 0.1841138789 |
| 363 | 0.1865258909 |
| 364 | 0.1889580013 |
| 365 | 0.1914102034 |
| 366 | 0.1938824876 |
| 367 | 0.1963748412 |
| 368 | 0.1988872485 |
| 369 | 0.2014196905 |
| 370 | 0.2039721450 |
| 371 | 0.2065445868 |
| 372 | 0.2091369872 |
| 373 | 0.2117493144 |
| 374 | 0.2143815332 |
| 375 | 0.2170336051 |
| 376 | 0.2197054884 |
| 377 | 0.2223971376 |
| 378 | 0.2251085043 |
| 379 | 0.2278395362 |
| 380 | 0.2305901778 |
| 381 | 0.2333603701 |
| 382 | 0.2361500503 |
| 383 | 0.2389591525 |
| 384 | 0.2417876068 |
| 385 | 0.2446353399 |
| 386 | 0.2475022750 |
| 387 | 0.2503883314 |
| 388 | 0.2532934250 |
| 389 | 0.2562174679 |
| 390 | 0.2591603684 |
| 391 | 0.2621220312 |
| 392 | 0.2651023574 |
| 393 | 0.2681012441 |
| 394 | 0.2711185848 |
| 395 | 0.2741542692 |
| 396 | 0.2772081831 |
| 397 | 0.2802802087 |
| 398 | 0.2833702242 |
| 399 | 0.2864781041 |
| 400 | 0.2896037190 |
| 401 | 0.2927469356 |
| 402 | 0.2959076169 |
| 403 | 0.2990856221 |
| 404 | 0.3022808062 |
| 405 | 0.3054930206 |
| 406 | 0.3087221129 |
| 407 | 0.3119679267 |
| 408 | 0.3152303017 |
| 409 | 0.3185090739 |
| 410 | 0.3218040752 |
| 411 | 0.3251151339 |
| 412 | 0.3284420742 |
| 413 | 0.3317847167 |
| 414 | 0.3351428780 |
| 415 | 0.3385163708 |
| 416 | 0.3419050042 |
| 417 | 0.3453085834 |
| 418 | 0.3487269096 |
| 419 | 0.3521597806 |
| 420 | 0.3556069901 |
| 421 | 0.3590683281 |
| 422 | 0.3625435811 |
| 423 | 0.3660325317 |
| 424 | 0.3695349588 |
| 425 | 0.3730506376 |
| 426 | 0.3765793398 |
| 427 | 0.3801208334 |
| 428 | 0.3836748827 |
| 429 | 0.3872412486 |
| 430 | 0.3908196885 |
| 431 | 0.3944099561 |
| 432 | 0.3980118017 |
| 433 | 0.4016249722 |
| 434 | 0.4052492111 |
| 435 | 0.4088842585 |
| 436 | 0.4125298512 |
| 437 | 0.4161857227 |
| 438 | 0.4198516033 |
| 439 | 0.4235272200 |
| 440 | 0.4272122967 |
| 441 | 0.4309065541 |
| 442 | 0.4346097101 |
| 443 | 0.4383214793 |
| 444 | 0.4420415734 |
| 445 | 0.4457697012 |
| 446 | 0.4495055688 |
| 447 | 0.4532488793 |
| 448 | 0.4569993330 |
| 449 | 0.4607566277 |
| 450 | 0.4645204585 |
| 451 | 0.4682905178 |
| 452 | 0.4720664958 |
| 453 | 0.4758480798 |
| 454 | 0.4796349552 |
| 455 | 0.4834268046 |
| 456 | 0.4872233089 |
| 457 | 0.4910241462 |
| 458 | 0.4948289931 |
| 459 | 0.4986375237 |
| 460 | 0.5024494104 |
| 461 | 0.5062643235 |
| 462 | 0.5100819317 |
| 463 | 0.5139019018 |
| 464 | 0.5177238991 |
| 465 | 0.5215475871 |
| 466 | 0.5253726280 |
| 467 | 0.5291986823 |
| 468 | 0.5330254096 |
| 469 | 0.5368524678 |
| 470 | 0.5406795140 |
| 471 | 0.5445062038 |
| 472 | 0.5483321923 |
| 473 | 0.5521571331 |
| 474 | 0.5559806796 |
| 475 | 0.5598024840 |
| 476 | 0.5636221980 |
| 477 | 0.5674394728 |
| 478 | 0.5712539591 |
| 479 | 0.5750653073 |
| 480 | 0.5788731673 |
| 481 | 0.5826771891 |
| 482 | 0.5864770224 |
| 483 | 0.5902723170 |
| 484 | 0.5940627228 |
| 485 | 0.5978478899 |
| 486 | 0.6016274687 |
| 487 | 0.6054011100 |
| 488 | 0.6091684651 |
| 489 | 0.6129291857 |
| 490 | 0.6166829246 |
| 491 | 0.6204293349 |
| 492 | 0.6241680710 |
| 493 | 0.6279000000 |
| 500 | 0.6537605648 |
| 510 | 0.6897667626 |
| 520 | 0.7243809408 |
| 530 | 0.7573108330 |
| 540 | 0.7883012600 |
| 550 | 0.8171416340 |
| 560 | 0.8436717536 |
| 570 | 0.8677855381 |
| 580 | 0.8894324667 |
| 590 | 0.9086166356 |
| 600 | 0.9253934985 |
| 610 | 0.9398645199 |
| 620 | 0.9521701040 |
| 630 | 0.9624812818 |
| 640 | 0.9709907059 |
| 650 | 0.9779035263 |
| 660 | 0.9834286938 |
| 670 | 0.9877711665 |
| 680 | 0.9911253836 |
* Probability represents probability at least six people will share at least one common birthday.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
April 6th, 2019 at 8:28:09 AM
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I think I mentioned that the R code I used was from a webpage that started with Mathematica code first and then the author converted that to R. I made some changes since but cannot find that original page.Quote: Wizard7Craps, that is some good stuff. I'm impressed you could calculate this much so fast. I'll have to look over your previous posts more carefully.
I found a page with the R code but it is different from what I remember.
https://stats.stackexchange.com/questions/333471/die-100-rolls-no-face-appearing-more-than-20-times
maybe searching the author can find both code versions as I remember the explanation and code was well done.
Someday I will clean it up and post it and give proper credit.
For the at least 6 people share a BDay, it uses the multinomial distribution for no more than 5 share and subtract from 1.
I now use Microsoft R Open 3.5.1 in my win 10 laptop as it is 10 times faster than basic R.
1826 0 1 0
> end.time <- Sys.time()
> print(end.time - start.time)
Time difference of 8.573598 secs
> trialsSeq <- 0:n
> meanBDay <- crossprod(trialsSeq,yesPdf)
> #meanBDay
> print(sprintf("For at least %g matches, %g: average number of people",m+1,meanBDay),quote=0)
[1] For at least 6 matches, 456.016: average number of people
here is a link to the text file code and results in Google Drive
https://drive.google.com/open?id=1EK6yXUEfgQxgZp2Y5C3IZm6n0Z1n10kM
winsome johnny (not Win some johnny)
April 6th, 2019 at 7:30:06 PM
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I'm afraid I don't know much about R code, in fact this thread is the first I've heard of it, to be honest. Perhaps it found a faster way to do simple math calculations, which are slow in C++, and this project is a perfect example. I hope we can discuss it over a beer sometime.
It took my program about a day to calculate the probability of 7 people not sharing a birthday out of 800 (6.23859%).
It took my program about a day to calculate the probability of 7 people not sharing a birthday out of 800 (6.23859%).
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
April 7th, 2019 at 12:43:12 AM
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A somewhat decent/easy approximation is to use Poisson distribution to determine the probability of any selected birthday having less than 7 hits after 800 draws, which is 99.268105%. Then take that to the 365th power to account for all birthdays which is 6.85%.Quote: Wizard
It took my program about a day to calculate the probability of 7 people not sharing a birthday out of 800 (6.23859%).
You can also use the binomial distribution to calculate the exact probability of any selected birthday having less than 7 hits after 800 draws, which is 99.277063%. Then take that to the 365th for 7.08%. But the Poisson calculation is much easier if you like to count with your fingers.
I was expecting more accuracy from this approximation since the results of the birthdays seem effectively independent in this scenario.
Last edited by: Ace2 on Apr 7, 2019
It’s all about making that GTA
April 8th, 2019 at 5:59:12 PM
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Those are both good ideas for finding estimates. I did the Poisson before and found it surprisingly accurate. However, perfectionists like me seek exact answers wherever possible.
My table below shows the probability a birthday common to seven or more people out of 600 is 43.143%. The Poisson estimate is 43.330%. Not bad.
Here are my results for seven people. This table took about five days of computer time. Until I learn R code, I'm taking this project off my desk for now.
My table below shows the probability a birthday common to seven or more people out of 600 is 43.143%. The Poisson estimate is 43.330%. Not bad.
Here are my results for seven people. This table took about five days of computer time. Until I learn R code, I'm taking this project off my desk for now.
| People | Common Birthday |
|---|---|
| 100 | 0.0000054175 |
| 200 | 0.0006086869 |
| 300 | 0.0084681973 |
| 400 | 0.0499840887 |
| 500 | 0.1780872266 |
| 600 | 0.4314305835 |
| 700 | 0.7383784089 |
| 800 | 0.9376140797 |
| 900 | 0.9943841169 |
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
April 8th, 2019 at 7:59:11 PM
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Quote: WizardI'm afraid I don't know much about R code, in fact this thread is the first I've heard of it, to be honest. Perhaps it found a faster way to do simple math calculations, which are slow in C++, and this project is a perfect example. I hope we can discuss it over a beer sometime.
It took my program about a day to calculate the probability of 7 people not sharing a birthday out of 800 (6.23859%).
I am surprised that you don't know much about R. It seems like the sort of thing that is right up your alley.
It is pretty easy to set up and play with, either directly or with a science and math distribution like Anaconda.
I am not sure about what online resources are out there for it, but here is one:
http://www.r-tutor.com/elementary-statistics/probability-distributions/poisson-distribution
April 8th, 2019 at 8:25:06 PM
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Trust me, I could teach a college course on Poisson. However, I will need to get up to speed on R.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
April 9th, 2019 at 7:31:21 AM
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many like also having arbitrary precision with computer calculations, and there are many good ones to select from.Quote: WizardHowever, perfectionists like me seek exact answers wherever possible.
here is a link to the R text file produced. (for at least 7 people)Quote: WizardMy table below shows the probability a birthday common to seven or more people out of 600 is 43.143%. The Poisson estimate is 43.330%. Not bad.
Here are my results for seven people. This table took about five days of computer time. Until I learn R code, I'm taking this project off my desk for now.
https://drive.google.com/open?id=1TVr6nrADb1RjS4AmdY4CgwSLskid_I6E
the end of the results for the mean
Time difference of 9.15665 secs
> trialsSeq <- 0:n
> meanBDay <- crossprod(trialsSeq,yesPdf)
> #meanBDay
> print(sprintf("For at least %g matches, %g: average number of people",m+1,meanBDay),quote=0)
[1] For at least 7 matches, 616.617: average number of people
You knowing C++ should easily grasp R (it is so basic - but not Basic)
R uses a lot of functions written in C, but base R is really simple and one does not need to know the code behind the function, but can if wants to.
I like , now, using pari/gp as I love the precision one can easily select.
R will produce results like this
7 1.0000000000000024425 -2.4424906541753443889e-15 -2.4424906541753443889e-15
I would suggest, IF you have a windows machine, to use Microsoft R Open 3.5.1
(on my dell i7 quad-core, 10 times faster than just R)
some even like using R Studio (helps with coding and such)
whatever the decision, thanks!
I may take you up on that beer offer in the future. (root beer)
winsome johnny (not Win some johnny)
April 9th, 2019 at 9:47:00 AM
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Thank you for all the suggestions! When things get a bit slow for me, I think I will indeed learn R. I already know several languages, so picking up new ones comes easily.
Do you mind if I use those numbers for 7 people sharing a birthday? Full credit to 7craps, of course.
Do you mind if I use those numbers for 7 people sharing a birthday? Full credit to 7craps, of course.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
April 9th, 2019 at 10:33:50 AM
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Quote: Dalex64I am surprised that you [Wizard] don't know much about R. It seems like the sort of thing that is right up your alley. It is pretty easy to set up and play with, either directly or with a science and math distribution like Anaconda.
Sorry coming a bit late to the party. I agree the Wiz is in for a pleasant surprise once he starts playing with R.
In my research I find it is increasingly common for journal articles to include links to the author's R code and to the raw data the author analyzed. This allows others to more easily review results of the research and how the author obtained those results. That often allows the reader to leverage the author's findings in their own research. The result has been an explosion of add-ins for R for hundreds of different, specialized applications, such as metallurgy and microbiology (and other equally diverse tool-sets).
Sort of an R newbie, myself, I was not aware of Anaconda until I read Dale's post. (Big thank-you, Dale!) R-Commander, another Anaconda-like add-on, provides more of an Excel-like user-interface some (non-programmers, perhaps) appreciate. (I find it gets in my way.)
I sure do enjoy it when the WoV stat sharpies use R to explore complex gaming mathematics. (Hint, hint!) WoV members have provided many great examples applying R to gaming questions. I know those gaming-related examples have helped me, and I expect the Wiz may also find them helpful. Perhaps, the Wiz will keep us posted as he plays with R. I sure hope so.
April 9th, 2019 at 11:20:39 AM
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R should be easy for you.Quote: WizardI already know several languages, so picking up new ones comes easily.
added: R is an interpreted language, it does not compile like C or C++ or even Excel vba. It can be real slow with for loops but there are ways to make those faster, maybe not as fast as C++. any code can be made to run slow... trying or not trying.
would be interesting to see what code you actually used.
Sure.Quote: WizardDo you mind if I use those numbers for 7 people sharing a birthday? Full credit to 7craps, of course.
I can also do 8 -10 people sharing if wanted and link to those.
I will do them later tonight and up to you if you want to use them.
(want to see if I can get arbitrary precision using R easily)
I did change some of the R code the original author had, just to have it my way for what I was after.
He (in the link provided knows his stuff and is a moderator at that other math site)
did change that page last year that I remember had both R and Mathematica. I hope I saved that page some place in a folder years ago. I just not have had time to get back to the code to see exactly how it works and have fun with it.
thanks again!
Last edited by: 7craps on Apr 9, 2019
winsome johnny (not Win some johnny)
