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slackyhacky
slackyhacky
Joined: Jan 18, 2012
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January 19th, 2015 at 10:05:46 AM permalink
Hey,
I will pay 3$ to paypal account for each question answered (or $50 for the whole kit and caboodle). However, I have to have some reassurance the answers are correct - perhaps verification from MathExtremist or Sally.

Anyway - here are the questions.

1) What is the probability (percentage) that a 10 will role 5 times before a 7 in 100 rolls? 1a) What about 4 times?

2) What is the probability that a 10 will role 5 times before a 7 in 1000 rolls? (assuming the answer to 1 is zero) 2a) What about 4 times?

3) How many times (with 95% confidence intervals or 2 STD) in 100 rolls will a 10 roll 5 times before a 7? 3a) or 4 times?

4) How many times (with 95% CI or 2 STD) in 1000 rolls will a 10 roll 5 times before a 7? 4a) or 4 times?


The next is harder to explain...let's see

5) After a 10 rolls once, what is the probability that a 4,5,6,8,9 (any combination) will roll 6 times before another 10 or a 7 rolls? 5a) What about 7 times? This is likely the same as asking what is the chance that a 4,5,6,8,9 rolls 6 (or 7) times before a 10 or 7.

6) After a 10 rolls twice, what is the probability 4,5,6,8,9 (or any combination) will roll 14 times before another 10 or a 7 rolls?

7) How many times in 1000 rolls can you expect that question 5 or 6 happens? In other words - lets assume that the answer to 4 is 3 times - so in 1000 rolls, a 10 rolls 5 times before a 7 three times. How many times in those 3 times could you expect that you would get a 4,5,6,8,9 rolling 7 or 14 times before the next 10? (I hope that made sense).

Oh, only one person gets the money.

Sheesh....
nodiceman
nodiceman
Joined: Jan 8, 2015
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January 19th, 2015 at 10:56:27 AM permalink
$50 wouldn't even let me buy odds on my PL bet.
phendricks
phendricks
Joined: Aug 1, 2014
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January 19th, 2015 at 11:37:24 AM permalink
5) If you want exactly six (and seven) times before a 10 or 7, the answers are 3.5% and 2.5%. If you wanted at least six (or seven) times, the answers are 11.8% and 8.2%.

6) Likewise, exactly 14 times before a 10 or 7, the answer is 0.2%. At least 14 times, the answer is 0.68%.
slackyhacky
slackyhacky
Joined: Jan 18, 2012
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January 19th, 2015 at 12:00:59 PM permalink
Quote: phendricks

5) If you want exactly six (and seven) times before a 10 or 7, the answers are 0.035 and 0.025. If you wanted at least six (or seven) times, the answers are 0.118 and 0.082.

6) Likewise, exactly 14 times before a 10 or 7, the answer is 0.002. At least 14 times, the answer is 0.0068



thanks.

and thanks for bringing up a point. I want to know "at least" instead of exactly. 11.8% sounds good.


I realize now I'm not sure I asked the question correctly.

I'll try again.

5) What is the chance of rolling a 4,5,6,8,9 six (or 7) times without rolling a 7, before two 10s?

Also, the next question is not worded correctly.

6) What is the chance of rolling a 4,5,6,8,9 fourteen times without rolling a 7 before 3 10s?
mustangsally
mustangsally
Joined: Mar 29, 2011
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January 19th, 2015 at 5:29:10 PM permalink
Quote: slackyhacky

1) What is the probability (percentage) that a 10 will role 5 times before a 7 in 100 rolls? 1a) What about 4 times?

hehe
I know what you are ups two (or two squared). I have just a few moments until snow man time
it might just help you out

for at least 5 in a row (5+)

and at least 4 in a row (4+) in 100 rolls


Quote: slackyhacky

2) What is the probability that a 10 will role 5 times before a 7 in 1000 rolls? (assuming the answer to 1 is zero) 2a) What about 4 times?


for at least 5 in a row (5+)

and at least 4 in a row (4+) in 1000 rolls



the others will have to wait for another day fur me (me eyes are tired)
burr fur
I love fur too
Sally

I think I got it right the 2nd time
I Heart Vi Hart
phendricks
phendricks
Joined: Aug 1, 2014
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January 19th, 2015 at 5:48:13 PM permalink
I believe the original poster is interested in 100 and 1000 rolls which include all outcomes (2 through 12). A simulation is probably most useful.

Otherwise, a simple binomial formula would be sufficient.

Also, you cannot simply quarter the number of trials just because 25 and 250 are the expected number of 10's and 7's.
mustangsally
mustangsally
Joined: Mar 29, 2011
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January 19th, 2015 at 7:29:28 PM permalink
Quote: phendricks

I believe the original poster is interested in 100 and 1000 rolls which include all outcomes (2 through 12). A simulation is probably most useful.

yes, It was useful as I did that also but did not show the results as a calculation I like much better.

Quote: phendricks

Otherwise, a simple binomial formula would be sufficient.

Also, you cannot simply quarter the number of trials just because 25 and 250 are the expected number of 10's and 7's.

well that is what I did so here is the actual probability weighted
for the number of 10s and 7s from 0 to 100

Excel easy math for 5+ in 100 rolls
0.057960619

the error looks to me to be small
0.00006850718

I took this from me Excel
please check my work as my fingers were still cold
# of 10s and 7srun5+ prob# of 10s and 7s probproduct
003.2072E-130
101.06907E-110
201.76396E-100
301.92076E-090
401.55261E-080
50.0041152269.93672E-084.08919E-10
60.0068587115.24438E-073.59697E-09
70.0096021952.34748E-062.2541E-08
80.0123456799.0965E-061.12302E-07
90.0150891633.09955E-054.67696E-07
100.0178326479.40196E-051.67662E-06
110.0205648420.0002564175.27318E-06
120.0232895090.000633921.47637E-05
130.026006650.0014303843.71995E-05
140.0287162640.0029629398.50845E-05
150.0314183510.0056625060.000177907
160.0341129120.0100273540.000342062
170.0367999770.0165156420.000607775
180.0394795670.0253851540.001002195
190.0421517020.0365189930.001539338
200.0448164040.049300640.002209477
210.0474736920.0626039880.002972042
220.0501235880.0749350760.003756015
230.0527661120.0847092170.004469776
240.0554012850.0905918010.005018902
250.0580291260.0917996920.005327056
260.0606496580.0882689340.005353481
270.0632628990.0806407550.005101568
280.0658688690.0700806560.004616134
290.0684675910.0579977840.003970969
300.0710590820.0457538080.003251224
310.0736433650.034438350.002536156
320.0762204570.0247525640.001886652
330.0787903810.0170017610.001339575
340.0813531550.0111678230.000908538
350.0839087990.0070197750.000589021
360.0864573340.0042248640.000365271
370.0889987790.0024359580.000216797
380.0915331540.0013461870.000123221
390.0940604780.0007133646.70994E-05
400.0965807710.0003626273.50228E-05
410.0990940530.0001768911.75289E-05
420.1016003428.283E-058.41555E-06
430.104099663.72414E-053.87682E-06
440.1065920241.60815E-051.71416E-06
450.1090774556.67085E-067.27639E-07
460.1115559722.65867E-062.96591E-07
470.1140275931.01821E-061.16105E-07
480.1164923383.74759E-074.36566E-08
490.1189502271.32568E-071.5769E-08
500.1214012774.50731E-085.47193E-09
510.1238455091.47298E-081.82422E-09
520.1262829414.62666E-095.84268E-10
530.1287135931.39673E-091.79778E-10
540.1311374824.05223E-105.314E-11
550.1335546281.12971E-101.50878E-11
560.135965053.02602E-114.11433E-12
570.1383687667.78625E-121.07737E-12
580.1407657951.92419E-122.7086E-13
590.1431561554.56587E-136.53632E-14
600.1455398661.04E-131.51362E-14
610.1479169452.27323E-143.36249E-15
620.1502874114.76645E-157.16338E-16
630.1526512839.58335E-161.46291E-16
640.1550085791.84679E-162.86268E-17
650.1573593163.40946E-175.3651E-18
660.1597035146.02682E-189.62505E-19
670.1620411911.01946E-181.65195E-19
680.1643723641.64913E-192.71071E-20
690.1666970512.54938E-204.24974E-21
700.1690152723.76337E-216.36067E-22
710.1713270445.30052E-229.08123E-23
720.1736323847.11644E-231.23564E-23
730.175931319.09865E-241.60074E-24
740.1782238421.10659E-241.97221E-25
750.1805099951.27873E-252.30823E-26
760.1827897891.40212E-262.56292E-27
770.185063241.45674E-272.6959E-28
780.1873303661.43184E-282.68227E-29
790.1895911861.32914E-292.51992E-30
800.1918457161.16299E-302.23115E-31
810.1940939749.57196E-321.85786E-32
820.1963359777.39298E-331.45151E-33
830.1985717435.34432E-341.06123E-34
840.2008012893.6053E-357.23948E-36
850.2030246332.26215E-364.59272E-37
860.2052417921.3152E-372.69934E-38
870.2074527827.05472E-391.46352E-39
880.2096576223.47392E-407.28333E-41
890.2118563281.56131E-413.30774E-42
900.2140489176.3609E-431.36154E-43
910.2162354062.33E-445.03828E-45
920.2184158137.59782E-461.65948E-46
930.2205901532.17859E-474.80575E-48
940.2227584455.40784E-491.20464E-49
950.2249207051.13849E-502.56071E-51
960.2270769491.97655E-524.48829E-53
970.2292271952.71691E-546.22789E-55
980.2313714592.77235E-566.41443E-57
990.2335097581.8669E-584.3594E-59
1000.2356421086.22302E-611.4664E-61
..total0.057960619


so, I thinks my pics have answers that are close enough for SH

SH, I think I also answered your Q 3 and 4 also
ask questions if you likes

but now
sex, drugs (your choice) and rock-n-roll time

see ya all at the Super Bowl
Sally Oh
I Heart Vi Hart
slackyhacky
slackyhacky
Joined: Jan 18, 2012
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January 20th, 2015 at 7:31:57 PM permalink
Mustangsally,

Love your math - but don't understand it.

I'll need some explanation how to interpret your spread sheet.

Tell me like I'm 10...
Zcore13
Zcore13
Joined: Nov 30, 2009
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January 20th, 2015 at 8:02:16 PM permalink
Quote: slackyhacky

Mustangsally,

Love your math - but don't understand it.

I'll need some explanation how to interpret your spread sheet.

Tell me like I'm 10...



You're not alone. I rarely understand anything she says. I think she's way smarter than me or something.


ZCore13
I am an employee of a Casino. Former Table Games Director,, current Pit Supervisor. All the personal opinions I post are my own and do not represent the opinions of the Casino or Tribe that I work for.
ThatDonGuy
ThatDonGuy
Joined: Jun 22, 2011
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January 20th, 2015 at 9:13:13 PM permalink
Could you clarify some of the problems?

Quote: slackyhacky


1) What is the probability (percentage) that a 10 will role 5 times before a 7 in 100 rolls? 1a) What about 4 times?


Is this asking what is the probability of 10 coming up 5 times both within 100 rolls and before 7 comes up at all?

Without the 100 roll restriction, the probability of 10 coming up once before 7 is 1/3, so the probability of it happening five times is (1/3)5 = 1/243. Even with the 100 roll restriction, it's very close to 1/243, as the probability of any particular roll not being 7 or 10 is 3/4, so the probability of 96 of them not being 7 or 10 is (100)C(96) x (3/4)96, or about 1/250,000.

Similarly, for 4 times, it would be close to (1/3)4 = 1/81.

Quote: slackyhacky


2) What is the probability that a 10 will role 5 times before a 7 in 1000 rolls? (assuming the answer to 1 is zero) 2a) What about 4 times?


These are closer to 1/243 and 1/81 than in 1 and 1a.

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