February 27th, 2013 at 9:50:40 AM
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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!

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!

Wisdom is the quality that keeps you out of situations where you would otherwise need it

February 27th, 2013 at 10:07:45 AM
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Quickly I want to say expected # of cards is 32, because the average value of each card is 0.5 points.

February 27th, 2013 at 11:17:54 AM
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Quote:dwheatleyI 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

February 27th, 2013 at 4:15:51 PM
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Thanks miplet, perfect.

Wisdom is the quality that keeps you out of situations where you would otherwise need it

February 27th, 2013 at 5:32:40 PM
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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

February 28th, 2013 at 3:00:02 AM
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Quote:dwheatleySince 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