antonadelson
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- Mar 4, 2013
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I asked this on math.stackexchange :
http://math.stackexchange.com/questions/320579/probability-question-involving-sets-of-cards
I have an infinite deck built out of sets of 10 cards (in other words 10*n cards). The sets are identical so one '2' is identical to another '2'.
A player draws 6 cards. If he draws:
What is the probability he won't win any points at all?
To expand on the problem, if the player gets a point for every pair he completes in a hand, what is the probability he'll get 1, 2, or even 3 points? (3 points being 6 cards of 3 completed pairs)
From what I know of Newton's Binomial, there are : binomiall[FONT=MathJax_Size2]([FONT=MathJax_Main]10 [/FONT][FONT=MathJax_Main]6[/FONT][FONT=MathJax_Size2])[/FONT][FONT=MathJax_Main]=[/FONT][FONT=MathJax_Main]210[/FONT] different hand combinations.[/FONT]
To expand even further, how do the probabilities change if the source deck ceases to be infinite? From trial and error I can see that if the deck has only 10 cards then the player has to draw at least 1 complete pair.
EDIT: For example, a hand of {1,1,3,5,5,9} will get no points. A hand of {1,1,2,3,4,5} will get 2.
EDIT2: Please don't forget the last question of how the size of the card deck changes those odds: e.g. the deck is of n*10 size. Or at least 40, or something...
http://math.stackexchange.com/questions/320579/probability-question-involving-sets-of-cards
I have an infinite deck built out of sets of 10 cards (in other words 10*n cards). The sets are identical so one '2' is identical to another '2'.
A player draws 6 cards. If he draws:
- any '1' AND a '2', or
- any '3' AND a '4', or
- any '5' AND a '6', or
- any '7' AND a '8', or
- any '9' AND a '10',
What is the probability he won't win any points at all?
To expand on the problem, if the player gets a point for every pair he completes in a hand, what is the probability he'll get 1, 2, or even 3 points? (3 points being 6 cards of 3 completed pairs)
From what I know of Newton's Binomial, there are : binomiall[FONT=MathJax_Size2]([FONT=MathJax_Main]10 [/FONT][FONT=MathJax_Main]6[/FONT][FONT=MathJax_Size2])[/FONT][FONT=MathJax_Main]=[/FONT][FONT=MathJax_Main]210[/FONT] different hand combinations.[/FONT]
To expand even further, how do the probabilities change if the source deck ceases to be infinite? From trial and error I can see that if the deck has only 10 cards then the player has to draw at least 1 complete pair.
EDIT: For example, a hand of {1,1,3,5,5,9} will get no points. A hand of {1,1,2,3,4,5} will get 2.
EDIT2: Please don't forget the last question of how the size of the card deck changes those odds: e.g. the deck is of n*10 size. Or at least 40, or something...