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:
#4/52#x#3/51##=##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#.