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Math Help - Bridge Hand

  1. #1
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    Bridge Hand

    What is the probability that a dealt bridge hand of 13 cards will contain no diamonds or hearts?


    Attempt 1: Divide possible outcomes by favorable outcome:

    I reasoned as follows. There are 52 choose 13 number of hands so this is the number of possible outcomes. I want to divide this by the number of hands containing only spades and clubs (in other words no diamonds or hearts). Thus, there are only 26 cards I can choose from to get these hands. So the favorable outcomes are 26 choose thirteen. The answer being (52 choose 13)/(26 choose 13).


    Do I have the right idea?
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  2. #2
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    Quote Originally Posted by divinelogos View Post
    What is the probability that a dealt bridge hand of 13 cards will contain no diamonds or hearts?


    Attempt 1: Divide possible outcomes by favorable outcome:

    I reasoned as follows. There are 52 choose 13 number of hands so this is the number of possible outcomes. I want to divide this by the number of hands containing only spades and clubs (in other words no diamonds or hearts). Thus, there are only 26 cards I can choose from to get these hands. So the favorable outcomes are 26 choose thirteen. The answer being (52 choose 13)/(26 choose 13).


    Do I have the right idea?
    That is the right idea, but you need to flip the fraction. The answer you gave is greater than 1.
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  3. #3
    MHF Contributor Unknown008's Avatar
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    Yep, otherwise, you'll end up with a probability greater than 1!
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  4. #4
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    hmm i think i have it right. it just means it's REALLY going to happen


    all kidding aside, thank you for the confirmation!
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