50 states, 10 at a time
April 2nd, 2012 at 6:47:20 PM
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Is it too late to add the welfare state ?
April 2nd, 2012 at 9:42:47 PM
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Quote: DocI would have missed a bunch of those, but I would have offered several other names, without being sure whether there are still countries by those names:Rhodesia
That name has been gone for about 3 decades. But in general I have little historical context for Africa. I have to struggle to think of the 54 names based on movies and news articles.
With the EU I have a historical context.
I start with BENELUX, one of the oldest historical economic unions. Basically they used to be a single land. That gives me three countries, Belgium, Netherlands, and Luxemburg.
Then the three great powers joined in the 1950's, France, Italy, and Germany (makes 6).
Then the three countries with very close historical ties: UK, Ireland, and Denmark (makes 9)
Then Greece: admired for founding European civilization (makes 10)
Then Spain and Portugal (makes 12):
Then Austria, Finland, Sweden (makes 15): the last of the traditional Western European nations with the exception of Iceland, Norway & Switzerland. I know these countries stayed out because of the natural resources or the Swiss tradition.
I remember the discussions about the "big bang" theory of bringing 10 applicants in at once. The decision was made that it would be less troublesome to bring in the stable portions of Eastern Europe all at once. Then I simply visualize the map in my mind: Latvia, Lithuania, Estonia, Poland, Hungary, Czechoslovakia, Slovakia, Slovenia, and Malta and Cyprus. (makes 25).
Then the poverty stricken duo of Romania and Bulgaria (makes 27).
So with a historical context, I can remember the 27 countries of the EU. The only one I continually confuse is Crete or Cyprus. I always forget which one is a country.
I'm sure I could come up with a mnemonic for learning the 54 countries of Africa, but I just never found it worth the trouble.
I remember an episode of the TV series Friends, where they challenged Ross to name all 50 states in 6 minutes. Of course, he thinks that is insanely easy. A half a dozen tries and he always ends up with 49 names.
I always remember one key historical fact. There were 15 free states, and 15 slave states until California was admitted as a free state. That broke the half century "standoff" and the country began to crumble politically (a process which took a decade). Given those subgroups, it isn't hard to remember all the states without forgetting one.
April 3rd, 2012 at 5:18:07 AM
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Quote: pacomartinThe only one I continually confuse is Crete or Cyprus. I always forget which one is a country.
In contrast, that's one I have a basis to remember. I have never visited Crete, but I did have the opportunity to do some consulting for the UN in Cyprus back in 1983. I was there on an issue of solar energy utilization, not the politics, and I have not kept up with the progress or lack thereof in the political situation. I had always assumed that eventually there would be reunification, which could be about as difficult economically and socially as the refugee situation was while I was there.
I had been slightly aware of the invasion when it occurred in 1974, but I had no idea at all of the role the US played. Like most Americans, I was not up on the various behind-the-scenes activities of our government, and they weren't/aren't covered extensively by the news media here. While I was in Cyprus, I accepted the version related by my Greek-Cypriot associates. When I got home, I asked a colleague from Turkey for his perspective. I told him what the Cypriots had said, and his reply was, "That's pretty much the way it was." That made it even more curious to me as to how I could receive such a warm welcome there. One of my Cypriot associates had explained, "We really like Americans. We just can't understand why you put up with your government."
April 3rd, 2012 at 9:41:15 AM
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Quote: pacomartinIceland, Norway & Switzerland. I know these countries stayed out because of the natural resources or the Swiss tradition.
I'd have always added Norway, but there we go, I'd be wrong!
Quote:I remember the discussions about the "big bang" theory of bringing 10 applicants in at once. The decision was made that it would be less troublesome to bring in the stable portions of Eastern Europe all at once. Then I simply visualize the map in my mind: Latvia, Lithuania, Estonia, Poland, Hungary, Czechoslovakia, Slovakia, Slovenia, and Malta and Cyprus. (makes 25).
It's the Czech Republic, which used to be half of Czechoslovakia.
I still await Transnistria's entrance into the EU.
"Then you can admire the real gambler, who has neither eaten, slept, thought nor lived, he has so smarted under the scourge of his martingale, so suffered on the rack of his desire for a coup at trente-et-quarante" - Honore de Balzac, 1829
May 27th, 2018 at 9:17:36 AM
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how good is that estimate?Quote: Wizard
Wizard partial credit version: Each box of cereal has one of 50 prizes inside. Each box has an equal chance of having each prize. You buy 210 boxes of cereal. What are the chances you will get all 50 prizes?
Here is my estimated answer.
It will take on average (50/50)+(50/49)+(50/48)+...+(50/2)+(50/1)=224.9602669 boxes to get all 50. The 50/50 is the number of boxes to get the first unique prize, 50/49 the second one, 50/48 the third, and so on.
I know this is not exactly appropriate, because success hasn't happen in 49 or less trials.
However, this is just an estimate.
The exponential distribution suggests that the probability of success within 210 units of time is 1-e^(210/224.96) = 60.68%.
and did you maybe provide an answer to a totally different question?
I know this is easy solved using a Markov chain.
it shows by and including 210 trials: p(success) 0.4739185789
another program I have shows this also
not even 50%
actually way way lower
some R code to run online if wanted
located here
https://sites.google.com/view/krapstuff/coupon-collecting/baseball-card-collector-problem
now for the OP question that is challenging
until completed.
I 1st used Excel too but wanted something faster
and easier to use for other similar type questions without re-doing Excel.
R code in the above online link
Sally
I Heart Vi Hart
May 27th, 2018 at 9:32:10 AM
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5th grade math question?Quote: DweenNOTE: This is not a homework question!
I am the substitute teacher for a 5th grade (10 year olds) class today. The plans from the regular teacher says that for a morning activity, each student should write down 10 U.S. states and capitals. There are 21 students in the class.
I posed a challenge: Without peeking or helping each other, can the entire class come up with all 50 states?
In other words, when combining all 210 states, will each of the 50 individual states be represented on the list?
Mathematically, here is the problem:
What is the probability that 21 people, each randomly choosing 10 different items from a list of 50, will have all 50 distinct items picked among their collective lists?
OMG!!
here is data from some R code using a Markov chain
I know inclusion exclusion can do this
but 5th grade math??
I get the same answer as a few others.
one can use the code here online for this or other type collecting problems
https://sites.google.com/view/krapstuff/coupon-collecting/baseball-card-collector-problem
the raised matrix (to the power of 21)
is interesting as it also shows that if the kids MISS the target for all 50 states,
49 would be the 2nd highest collected. that is interesting too.
"Missed it by that much!"
here that is 1st.
after all 21 kids papers have been counted. drum roll please (hehe)
> print(formatC(as.matrix(M[1, ]), digits=9),quote=FALSE)
[,1]
0 0
1 0
2 0
3 0
4 0
5 0
6 0
7 0
8 0
9 0
10 5.84338594e-201
11 1.57245514e-178
12 1.1210833e-161
13 7.7400217e-148
14 5.44809658e-136
15 1.36773635e-125
16 2.63811559e-116
17 6.52667929e-108
18 2.97691431e-100
19 3.27261324e-93
20 1.0637839e-86
21 1.19979421e-80
22 5.33501247e-75
23 1.03754177e-69
24 9.61261193e-65
25 4.55603276e-60
26 1.17298039e-55
27 1.72609017e-51
28 1.51635516e-47
29 8.25544932e-44
30 2.87669768e-40
31 6.59759176e-37
32 1.02027695e-33
33 1.08639194e-30
34 8.11038878e-28
35 4.31140798e-25
36 1.65361807e-22
37 4.62650932e-20
38 9.52625496e-18
39 1.45338953e-15
40 1.65058372e-13
41 1.39857132e-11
42 8.83843114e-10
43 4.15134966e-08
44 1.43832504e-06
45 3.62842998e-05
46 0.000652511935
47 0.00808282723
48 0.0650487684
49 0.304022186
50 0.622155941
21 kids at 10 states each: p(success) 0.622155941
the average wait time is also shown starting with X number of states (0)
> coupons.r(50,10,100)
Time difference of 0.07811904 secs
draw Prob on X cumulative
[1,] 4 0 0
[2,] 5 4.225964563e-19 4.225964563e-19
[3,] 6 1.670820982e-11 1.670821024e-11
[4,] 7 4.054531454e-08 4.056202275e-08
[5,] 8 4.648150735e-06 4.688712757e-06
[6,] 9 0.0001076206172 0.0001123093299
[7,] 10 0.0009339056095 0.001046214939
[8,] 11 0.00423056663 0.005276781569
[9,] 12 0.01222578825 0.01750256982
[10,] 13 0.02566097801 0.04316354782
[11,] 14 0.04269418628 0.0858577341
[12,] 15 0.05983352164 0.1456912557
[13,] 16 0.07374884418 0.2194400999
[14,] 17 0.08248723373 0.3019273337
[15,] 18 0.08567118838 0.387598522
[16,] 19 0.08405214008 0.4716506621
[17,] 20 0.07891151885 0.550562181
[18,] 21 0.07159376002 0.622155941
[19,] 22 0.06324406991 0.6854000109
[20,] 23 0.05471318232 0.7401131932
[21,] 24 0.04656314676 0.78667634
[22,] 25 0.03911910652 0.8257954465
[23,] 26 0.03253251428 0.8583279608
[24,] 27 0.02683846312 0.8851664239
[25,] 28 0.0220008268 0.9071672507
[26,] 29 0.01794471289 0.9251119636
[27,] 30 0.01457818965 0.9396901532
[28,] 31 0.01180588249 0.9514960357
[29,] 32 0.009536839026 0.9610328747
[30,] 33 0.007688576956 0.9687214517
[31,] 34 0.00618872004 0.9749101717
[32,] 35 0.004975195163 0.9798853669
[33,] 36 0.003995634621 0.9838810015
[34,] 37 0.003206392368 0.9870873939
[35,] 38 0.002571422448 0.9896588163
[36,] 39 0.002061162226 0.9917199786
[37,] 40 0.001651495903 0.9933714745
[38,] 41 0.001322832545 0.994694307
[39,] 42 0.001059308571 0.9957536156
[40,] 43 0.0008481111539 0.9966017267
[41,] 44 0.0006789121459 0.9972806389
[42,] 45 0.0005433993193 0.9978240382
[43,] 46 0.0004348911821 0.9982589294
[44,] 47 0.0003480223211 0.9986069517
[45,] 48 0.0002784875156 0.9988854392
[46,] 49 0.0002228343744 0.9991082736
[47,] 50 0.0001782957503 0.9992865694
[48,] 51 0.0001426545905 0.9994292239
[49,] 52 0.0001141351285 0.9995433591
[50,] 53 9.131539773e-05 0.9996346745
[51,] 54 7.30569634e-05 0.9997077314
[52,] 55 5.844852862e-05 0.99976618
[53,] 56 4.676070635e-05 0.9998129407
[54,] 57 3.740976438e-05 0.9998503504
[55,] 58 2.992857516e-05 0.999880279
[56,] 59 2.394334638e-05 0.9999042224
[57,] 60 1.915498672e-05 0.9999233773
[58,] 61 1.532418652e-05 0.9999387015
[59,] 62 1.225947475e-05 0.999950961
[60,] 63 9.807659728e-06 0.9999607687
[61,] 64 7.846178677e-06 0.9999686148
[62,] 65 6.276975349e-06 0.9999748918
[63,] 66 5.021600913e-06 0.9999799134
[64,] 67 4.017293869e-06 0.9999839307
[65,] 68 3.213843461e-06 0.9999871446
[66,] 69 2.571080096e-06 0.9999897156
[67,] 70 2.056867469e-06 0.9999917725
[68,] 71 1.645496135e-06 0.999993418
[69,] 72 1.316398283e-06 0.9999947344
[70,] 73 1.053119502e-06 0.9999957875
[71,] 74 8.42496159e-07 0.99999663
[72,] 75 6.739972822e-07 0.999997304
[73,] 76 5.391980518e-07 0.9999978432
[74,] 77 4.313585854e-07 0.9999982746
[75,] 78 3.450869599e-07 0.9999986197
[76,] 79 2.760696263e-07 0.9999988957
[77,] 80 2.208557382e-07 0.9999991166
[78,] 81 1.766846142e-07 0.9999992933
[79,] 82 1.413477064e-07 0.9999994346
[80,] 83 1.130781747e-07 0.9999995477
[81,] 84 9.04625459e-08 0.9999996381
[82,] 85 7.237004061e-08 0.9999997105
[83,] 86 5.789603496e-08 0.9999997684
[84,] 87 4.631682955e-08 0.9999998147
[85,] 88 3.705346464e-08 0.9999998518
[86,] 89 2.964277235e-08 0.9999998814
[87,] 90 2.371421829e-08 0.9999999051
[88,] 91 1.897137489e-08 0.9999999241
[89,] 92 1.517710008e-08 0.9999999393
[90,] 93 1.214168017e-08 0.9999999514
[91,] 94 9.7133442e-09 0.9999999611
[92,] 95 7.770675403e-09 0.9999999689
[93,] 96 6.216540349e-09 0.9999999751
[94,] 97 4.973232297e-09 0.9999999801
[95,] 98 3.978585848e-09 0.9999999841
[96,] 99 3.182868686e-09 0.9999999873
[97,] 100 2.546294953e-09 0.9999999898
avg draws
0 20.839350
1 20.748714
2 20.656228
3 20.561816
4 20.465394
5 20.366876
6 20.266169
7 20.163174
8 20.057783
9 19.949882
10 19.839350
11 19.726055
12 19.609855
13 19.490597
14 19.368115
15 19.242232
16 19.112751
17 18.979463
18 18.842135
19 18.700516
20 18.554328
21 18.403268
22 18.246999
23 18.085148
24 17.917303
25 17.743003
26 17.561730
27 17.372905
28 17.175870
29 16.969878
30 16.754078
31 16.527487
32 16.288971
33 16.037203
34 15.770626
35 15.487388
36 15.185267
37 14.861566
38 14.512965
39 14.135314
40 13.723332
41 13.270150
42 12.766616
43 12.200139
44 11.552737
45 10.797438
46 9.891082
47 8.758034
48 7.247191
49 5.000000
>
I know
Sally
I Heart Vi Hart
May 27th, 2018 at 11:46:13 AM
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Ah,, mustang Sally.
Missed your math posts but most of all I'm on a computer that won't play youtube so its been a long time since I've seen any of those Vi Hart videos.
Welcome back.
Missed your math posts but most of all I'm on a computer that won't play youtube so its been a long time since I've seen any of those Vi Hart videos.
Welcome back.
May 27th, 2018 at 2:34:41 PM
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If someone were to randomly select 1 out of 50 states 210 times (with replacement), the expected number of selections would be ( Ln (50) + .577 ) * 50 = 224. The expected number in this case will be slightly lower since each student will make 10 selections with no repeats. I estimate the number to be around 210, which makes me wonder if the OP is fishing.
With an expected value of 210 then the chance of getting all 50 with as many tries would be around 1 - 1/e.
With an expected value of 210 then the chance of getting all 50 with as many tries would be around 1 - 1/e.
It’s all about making that GTA
May 27th, 2018 at 2:52:15 PM
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that number using the Markov chain is aboutQuote: Ace2The expected number in this case will be slightly lower since each student will make 10 selections with no repeats.
20.839350
looks to be slightly less (but close) than 224.96027 (coupon collecting 1 at a time) divided by 10
22.49
21 students is right there in the teachers class.
makes one wonder if he already had the answer (or an answer)
and ONLY 21 kids in class?
small class size I due say so
I just came to the party, to rest!
Sally
I Heart Vi Hart
