What's the probability of getting at least 3 aces in a 13-card hand from a standard deck of cards?

You probably need to use combinatorics to solve this. You needn't give me the exact answer, but please show your work so I can see how to solve it!

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  • 1 decade ago
    Best Answer

    Chance of getting dealt an ace is 4/52 (or 1/13)

    Since you are getting dealt 13 cards:

    13 * (1/13) = 1

    So you have a 100% chance in getting dealt one ace. Now for the second ace. The chance is now 3/52.

    Since one of your cards is already an ace...you are only dealt 12 cards.

    12*(3/52) = 9/13

    Now there are only 2 aces left and 11 chances that you will get dealt one. So 2/52 (number of aces/number of cards left).

    11*(1/26) = 11/26

    Now,

    1 * (9/13) * (11/26) = 99/338 or about a 29.28994% chance

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