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What is the probability of drawing AT LEAST one ace, when drawing 13 cards?

When working with a deck that is missing one non-ace. So I am drawing from a deck of 51 cards. And a description would be nice :)

3 Answers

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  • M3
    Lv 7
    1 decade ago
    Favorite Answer

    there are only 51 cards which include 4 aces

    ways of not drawing an ace = 47C13

    ways of drawing any 13 cards = 51C13

    so P[ no ace ] = 47C13 / 51C13

    and P[ at least one ace ] = 1 - 47C13 / 51C13

    = 0.7046

    ------------

  • ?
    Lv 7
    1 decade ago

    The odds of NOT drawing an ace on the first card (47/51) is multiplied by the chances of NOT drawing an ace on the second card (46/50) multiplied by then chances of NOT drawing an ace on the third card (45/49) etc., etc., etc., all the way to the 13th card. (35/39)

    The product of all multiplying all 13 of these fractions is: .2953782

    That's the chances of NOT drawing an ace. Subtract this from 1 to find the probability OF drawing an ace. 1 - .2953782 = .7046218. That's your answer. 70.46218%

  • 1 decade ago

    ok so u have 4/51 for one so 51-13 is 38 so go 4/38 then u get 2/19 so that should be the answer

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