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Math Help - card probability

  1. #1
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    Question card probability

    Need help with this problem in a hurry

    If 2 cards are drawn from a deck of 52 cards and not replaced, what is the probability that both cards will be hearts?
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by Beth shaske View Post
    Need help with this problem in a hurry

    If 2 cards are drawn from a deck of 52 cards and not replaced, what is the probability that both cards will be hearts?
    If I remember correctly the is a reduced samplespace problem.

    the prob of drawing the first heart is

    \frac{13}{52}=\frac{1}{4}

    To draw the next heart the is

    \frac{12}{51}=\frac{4}{17}

    This is because of the 51 cards left 11 are hearts.

    The the probability is \frac{1}{4} \cdot \frac{4}{17}=\frac{1}{17}

    I hope this helps
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  3. #3
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    Hello, Beth!

    Another approach . . .


    If 2 cards are drawn from a deck of 52 cards and not replaced,
    what is the probability that both cards will be Hearts?
    There are: . {52\choose2} = 1326 possible outcomes.

    There are: . {13\choose2} = 78 ways to draw two Hearts.

    Therefore: . P(\text{2 Hearts}) \;=\;\frac{78}{1326} \;=\;\boxed{\frac{1}{17}}

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