Two cards are drawn from a well-shuffled ordinary deck of 52 cards. What is the probability that they are both aces if the first card is not replaced?

2 Answers
Mar 20, 2018

0.00452

-OR-

0.452%

Explanation:

There are 52 cards in a deck, and there are 4 aces in a deck, so the probability of drawing an ace is 4/52

If you do not replace the card, there are only 51 cards left and only 3 aces left, so the probability of now drawing an ace is 3/52

Multiply these probabilities:
4/52x3/51=12/2652->0.00452

Mar 20, 2018

1/169

Explanation:

The probability that the first card is an ace is 4/52=1/13. The probability that the second card is an ace is 4/52=1/13.

Therefore, the probability that both cards are aces is 1/13*1/13=1/169.