dwheatley
• Posts: 1246
Joined: Nov 16, 2009
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
• Posts: 145
Joined: Apr 15, 2011
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
• Posts: 2127
Joined: Dec 1, 2009
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	Probability13	0.00000002856166614	0.00000034048214915	0.00000217697775216	0.0000098995985317	0.00003584401807518	0.00010973985148219	0.00029473533028220	0.00071156713222821	0.00157077410184722	0.00320963662841123	0.00612545877598824	0.0109899888765325	0.01862192559634226	0.02988730463702727	0.04549427213498428	0.06565447900264429	0.08960587521488530	0.11504226323960731	0.13758912655971532	0.15062388591800433	0.14598930481283434	0.11652661064425835	0.061904761904762`
“Man Babes” #AxelFabulous
dwheatley
• Posts: 1246
Joined: Nov 16, 2009
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
• Posts: 1246
Joined: Nov 16, 2009
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
• Posts: 2127
Joined: Dec 1, 2009
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	Probability13	0.00000018999716714	0.00000222178505715	0.00001390716639416	0.00006176877605317	0.00021784523697418	0.0006475426689619	0.00168198583221120	0.0039088289956421	0.00825791021539922	0.01603230642743123	0.02880471054795224	0.04807316771721725	0.07456803856136426	0.1071560993696727	0.14144905273937528	0.16856825043699329	0.17515294771968930	0.14677419354838731	0.078629032258064`

40 cards
`Card	Probability13	0.00000000548481514	0.00000006626099615	0.00000042982850716	0.00000198561379417	0.0000073141945618	0.00002282008019419	0.00006257941097820	0.00015461194549121	0.00035020321449722	0.00073655412921323	0.00145231438334924	0.00270437289347225	0.00478259126757526	0.00806702141518627	0.01301973354253728	0.02015109022895429	0.02994881700387830	0.04275860300528231	0.05860877480896532	0.07698100577357533	0.09654701140769234	0.11492164433340935	0.12853078642552336	0.13276434329065937	0.12268847795163638	0.09473684210526339	0.05`
“Man Babes” #AxelFabulous