dwheatley
dwheatley
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February 27th, 2013 at 9:50:40 AM permalink
I have a special deck of cards, with only 0, 1 and 2 written on the cards. There are 21 x 0 , 12 x 1, and 3 x 2. (36 cards, totaling 18 points).

I flip cards one at a time, until I have revealed cards that total 16 points or more.

What is the expected number of cards I have to reveal until I hit 16 or more? If X is the number of cards it takes, what is P( X <= 22)?
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I'm pretty sure that simulation is the way to go. I can program it, but I was hoping someone else here can slam it out faster than I can. Thanks for your help!
Wisdom is the quality that keeps you out of situations where you would otherwise need it
jc2286
jc2286
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February 27th, 2013 at 10:07:45 AM permalink
Quickly I want to say expected # of cards is 32, because the average value of each card is 0.5 points.
miplet
miplet
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February 27th, 2013 at 11:17:54 AM permalink
Quote: dwheatley

I have a special deck of cards, with only 0, 1 and 2 written on the cards. There are 21 x 0 , 12 x 1, and 3 x 2. (36 cards, totaling 18 points).

I flip cards one at a time, until I have revealed cards that total 16 points or more.

What is the expected number of cards I have to reveal until I hit 16 or more? If X is the number of cards it takes, what is P( X <= 22)?
-------
I'm pretty sure that simulation is the way to go. I can program it, but I was hoping someone else here can slam it out faster than I can. Thanks for your help!


:) why simulate when you can be exact

Cards Probability
13 0.000000028561666
14 0.000000340482149
15 0.000002176977752
16 0.00000989959853
17 0.000035844018075
18 0.000109739851482
19 0.000294735330282
20 0.000711567132228
21 0.001570774101847
22 0.003209636628411
23 0.006125458775988
24 0.01098998887653
25 0.018621925596342
26 0.029887304637027
27 0.045494272134984
28 0.065654479002644
29 0.089605875214885
30 0.115042263239607
31 0.137589126559715
32 0.150623885918004
33 0.145989304812834
34 0.116526610644258
35 0.061904761904762
“Man Babes” #AxelFabulous
dwheatley
dwheatley
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February 27th, 2013 at 4:15:51 PM permalink
Thanks miplet, perfect.
Wisdom is the quality that keeps you out of situations where you would otherwise need it
dwheatley
dwheatley
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February 27th, 2013 at 5:32:40 PM permalink
Since you seem to have a magic box that spits out exact probabilities, can you also find me the numbers for a 40 card deck with 4 extra 0s, and a 32 card deck with 4 less 0s? Please & Thank you.
Wisdom is the quality that keeps you out of situations where you would otherwise need it
miplet
miplet
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February 28th, 2013 at 3:00:02 AM permalink
Quote: dwheatley

Since you seem to have a magic box that spits out exact probabilities, can you also find me the numbers for a 40 card deck with 4 extra 0s, and a 32 card deck with 4 less 0s? Please & Thank you.


My magic box came up with the following. (How come you don't have your own google docs spread sheet magic box? They can come in handy at times. Of course it does help to use it properly.)
36 cards

Card Probability
13 0.000000189997167
14 0.000002221785057
15 0.000013907166394
16 0.000061768776053
17 0.000217845236974
18 0.00064754266896
19 0.001681985832211
20 0.00390882899564
21 0.008257910215399
22 0.016032306427431
23 0.028804710547952
24 0.048073167717217
25 0.074568038561364
26 0.10715609936967
27 0.141449052739375
28 0.168568250436993
29 0.175152947719689
30 0.146774193548387
31 0.078629032258064

40 cards

Card Probability
13 0.000000005484815
14 0.000000066260996
15 0.000000429828507
16 0.000001985613794
17 0.00000731419456
18 0.000022820080194
19 0.000062579410978
20 0.000154611945491
21 0.000350203214497
22 0.000736554129213
23 0.001452314383349
24 0.002704372893472
25 0.004782591267575
26 0.008067021415186
27 0.013019733542537
28 0.020151090228954
29 0.029948817003878
30 0.042758603005282
31 0.058608774808965
32 0.076981005773575
33 0.096547011407692
34 0.114921644333409
35 0.128530786425523
36 0.132764343290659
37 0.122688477951636
38 0.094736842105263
39 0.05
“Man Babes” #AxelFabulous
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