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Math Help - Probability Basic

  1. #1
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    Probability Basic

    In the game of bridge, each player is dealt 13 cars out of a deck of 52. determine the probability of a player receiving
    a) all hearts
    b) all hearts in ascending order
    Can someone check my work? there arent any in my text

    a)
    13C13/52C13
    b) 13P13/52C13
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  2. #2
    Junior Member SirOJ's Avatar
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    ye your spot on there
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  3. #3
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    Hello john-1
    Quote Originally Posted by john-1 View Post
    In the game of bridge, each player is dealt 13 cars out of a deck of 52. determine the probability of a player receiving
    a) all hearts
    b) all hearts in ascending order
    Can someone check my work? there arent any in my text

    a)
    13C13/52C13
    b) 13P13/52C13
    Your answer to (a) is fine: the number of ways of choosing 13 cards from 52 is {^{52}C_{13}}. Just one of these consists of all 13 hearts. So the probability is \frac{1}{{^{52}C_{13}}}.

    But I think you've confused things in part (b). The number of ways of choosing and arranging 13 cards from 52 is {^{52}P_{13}}, and again just one of these is all 13 hearts in ascending order. So the probability is \frac{1}{{^{52}P_{13}}}.

    Grandad
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    Quote Originally Posted by Grandad View Post
    So the probability is \frac{1}{{^{52}P_{13}}}.
    While I agree that is most likely the expected answer, I would have said it is \frac{2}{{^{52}P_{13}}}.
    The ace could be first or last.
    At least that is true in poker. I do not know bridge.
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  5. #5
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    Quote Originally Posted by Plato View Post
    While I agree that is most likely the expected answer, I would have said it is \frac{2}{{^{52}P_{13}}}.
    The ace could be first or last.
    At least that is true in poker. I do not know bridge.
    Yes, I realised that the phrase 'ascending order' could be ambiguous, but I assumed that, since it is bridge, aces were always high, and that there was therefore only one possibility.

    Grandad
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