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Math Help - Actuary Probability problem

  1. #1
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    Actuary Probability problem

    The game of bridge is played by four players: north, south, east and west.
    Each of these players receive 13 cards.
    (a) What is the probability that one of the players receives all 13 spades?

    I am having serious trouble with this one, the answer in the back of the book is 6.3  10^-12 and I cant seem to match it.

    At first I thought it may be C(13,13)/C(52,13) but thats considering only one player.

    Then I thought maybe C(13,13)*C(39,13)*C(26,13)*(13,13)/C(52,52) but this does not work either.

    Help!!
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  2. #2
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    Re: Actuary Probability problem

    Quote Originally Posted by feefers View Post
    The game of bridge is played by four players: north, south, east and west.
    Each of these players receive 13 cards.
    (a) What is the probability that one of the players receives all 13 spades?

    There are \frac{52!}{(13!)^4} ways to deal a bridge game.

    There are 4\cdot \frac{39!}{(13!)^3} ways for one player to receive all 13 spades.
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  3. #3
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    Re: Actuary Probability problem

    Another way to look at the problem:

    There are N = \binom{52}{13} possible bridge hands. Only one of these has all the spades. So the probability that one of the players has all the spades is 4 / N.
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