Question

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?

Answer 1

`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`

Answer 2

`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`.