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Thread: Card Probability

  1. #1
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    Card Probability




    Just want to make sure what im doing is correct.

    Out of a deck of 52 cards, 12 cards are selected at random w/o replacement, what is the probability of exactl 3 spades and 4 hearts ?

    This is what i have so far,

    ((13/52)(12/51)(11/50)+(13/49)(12/48)(11/47)(10/46))/(52choose12)

    But something doesnt seem right
    Last edited by ITman95; 11-20-2013 at 03:23 PM.

  2. #2
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    Re: Card Probability

    OR is the correct answer as follows:

    ((13/52)(12/51)(11/50)(13/49)(12/48)(11/47)(10/46)/(52choose12)

    OR

    52c12 = possible 12 card hands
    13c4=possible 4 diamonds
    13c3=possible 3 heart
    ((13c3)(13c4))/(52c12)
    Last edited by ITman95; 11-20-2013 at 03:59 PM.

  3. #3
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    Re: Card Probability

    You have exactly 3 hearts and 4 spades out of 12 cards, therefore you need 5 cards from (clubs or diamonds) to fill the rest.

    \frac {\displaystyle \binom {13} {3} \binom {13} {4} \binom {26} {5}} 
{\displaystyle \binom {52} {12}}

  4. #4
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    Re: Card Probability


    Alright, Thanks for the help at least i was close sort of...i wasnt sure about (26c5)

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