Question

three cards are drawn all at once from a standard deck of 52 playing cards. What is the probability of selecting exactly two aces?

Answer 1

There are 4 aces in a standard 52 card deck. So the probability of getting an ace on the first try is 4/52, or 1/13 (simplified). The probability of getting it the second time after you pulled one out is 3/51 because you removed one, or 1/17 (simplified). The probability of NOT getting a ace on the third go is 48/50, because there are 50 remaining cards and 2 of them remain to be aces. Simplified probability of not getting it is 24/25. Multiply these probabilities together to find the exact probability of getting exactly two aces.

1/13 * 1/17 * 24/25 = 24/5525 or 0.0043438914027149.

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