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Math Help - Card Probability Questions?

  1. #1
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    Card Probability Questions?

    Suppose you have a deck of 52 cards. You are to draw one card. Assume each card has a probability of 1/52 of being drawn. What is the probability that you will draw:

    a)The ace of spades?
    b) The ace of spades of the queen of hearts?
    c) An ace or a spade?
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  2. #2
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    Re: Card Probability Questions?

    Hello, allstar2!

    This is a simple matter of Counting.
    Exactly where is your difficulty?


    Suppose you have a deck of 52 cards. .You are to draw one card.
    Assume each card has a probability of 1/52 of being drawn.
    P(\text{any particular card}) \:=\:\frac{1}{52}


    What is the probability that you will draw:

    a) the Ace of Spades?
    P(A\spadesuit) \:=\:\frac{1}{52}



    b) the Ace of Spades or the Queen of Hearts?
    P(A\spadesuit \vee Q\heartsuit) \:=\:\frac{2}{52} \:=\:\frac{1}{26}



    c) an Ace or a Spade?
    How many outcomes are "winners?

    A\heartsuit,\,A\clubsuit,\,A\diamondsuit,\,A \spadesuit,\,2\spadesuit,\,3\spadesuit,\,4 \spadesuit,\,5\spadesuit,\,6\spadesuit,\,7 \spadesuit,\,8\spadesuit,\,9\spadesuit,\,10 \spadesuit,\,J\spadesuit,\,Q\spadesuit,\,K \spadesuit
    . . (16 outcomes)

    Therefore: . P(A \vee \spadesuit) \:=\:\frac{16}{52} \:=\:\frac{4}{13}

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