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Math Help - 2 face cards not drawn, with replacement

  1. #1
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    2 face cards not drawn, with replacement

    Using a standard deck, find the probability that two face cards are not drawn, with replacement.

    My first thought is that this can be done in 3 ways, no face cards, and one face card as either the first or second card drawn.

    P(No face cards) = 40/52 * 40/52
    P(No face card then a face card)= 40/52 * 12/52
    P(Face card then no face card)= 12/52 * 40/52

    Add them all up and get 160/169

    My second thought is to find the complement.

    1 - P(two face cards) = 1 - (12/52 * 12/52)
    = 1 - 9/169
    = 160/169

    I'm thrilled that I got the same number, but I am tired and need someone to check over it... Please and thank you.
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  2. #2
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    Quote Originally Posted by tcRom View Post
    Using a standard deck, find the probability that two face cards are not drawn, with replacement.

    My first thought is that this can be done in 3 ways, no face cards, and one face card as either the first or second card drawn.

    P(No face cards) = 40/52 * 40/52
    P(No face card then a face card)= 40/52 * 12/52
    P(Face card then no face card)= 12/52 * 40/52

    Add them all up and get 160/169

    My second thought is to find the complement.

    1 - P(two face cards) = 1 - (12/52 * 12/52)
    = 1 - 9/169
    = 160/169

    I'm thrilled that I got the same number, but I am tired and need someone to check over it... Please and thank you.
    Looks OK. The second method is the best approach.
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