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Math Help - poker probability

  1. #1
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    poker probability

    A standard 52 card deck is well shuffled and the cards are drawn one at a time and without replacement until a king or queen is drawn. Determine the following probabilities.

    a) What is the probability that at least 4 cards are drawn before the first king or queen occurs?

    b) Given that a king or queen does not occur in the first 5 cards drawn, what is the probability that a king or queen occurs in 3 or fewer more draws?
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  2. #2
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    Quote Originally Posted by digitalis77 View Post
    A standard 52 card deck is well shuffled and the cards are drawn one at a time and without replacement until a king or queen is drawn. Determine the following probabilities.

    a) What is the probability that at least 4 cards are drawn before the first king or queen occurs?
    This is the probability that none of the first four cards are a K or Q.

    There are 44 cards which are not a K or Q

    Thus the probability that the fiorst card is not a K or Q is 44/52
    The probability that the second is not a K or Q is 43/51 (as after the first card is drawn there are 51 remaining of which 43 are not K or Q.

    .. and so on for the third and fouth card.

    The final probability is the product of the four probabilities you will have calculated.

    b) Given that a king or queen does not occur in the first 5 cards drawn, what is the probability that a king or queen occurs in 3 or fewer more draws?
    After drawing 5 cards none of which are a K or Q, you have a deck with 47 cards of which 39 are not a K or Q.

    The required probability here is 1 minus the probability that none of the first three cards is a K or Q. This klatter probability can be calculated using the technique of part (a).

    RonL
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