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Thread: Card draw and joint probability

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    Re: Card draw and joint probability




    Thanks fellas. I think I've got the original question nailed.

    I'm now expanding it to include the probability of drawing an Ace, a 3 and a 9 (from a draw of 5 cards). I've long-handed the calculation and got 2.388%. Can someone confirm?

    I'm screwing up the complement calculation though...grrr

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    Re: Card draw and joint probability

    The probability of drawing exactly one Ace, one 3 and one 9 out of five cards is

    \frac {\displaystyle \binom {4} {1} \binom {4} {1} \binom {4} {1} \binom {40} {2}}{\displaystyle \binom {52} {5}}

    i.e. you just consider as 4 groups.

  3. #18
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    Re: Card draw and joint probability


    Quote Originally Posted by BGM View Post
    The probability of drawing exactly one Ace, one 3 and one 9 out of five cards is

    \frac {\displaystyle \binom {4} {1} \binom {4} {1} \binom {4} {1} \binom {40} {2}}{\displaystyle \binom {52} {5}}

    i.e. you just consider as 4 groups.
    Thanks.

    This calculation was no problem. For reasons I can't explain, I'm screwing up the complement calculation though (i.e. 100% less the probability of drawing zero of those 3 cards should equal the probability of drawing at least 1 of each...)

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