# Two cards are chosen from a deck of 52 cards without replacement.

Two cards are chosen from a deck of 52 cards without replacement.

Determine the probability that both cards are face cards or both cards are hearts?

I did face cards $\frac{12}{52} \times \frac{11}{51}$ + hearts $\frac{13}{52} \times \frac{12}{51}$

How do I solve for when both cards are face cards and hearts so I can subtract the overlap?

## 2 Answers

For face cards that are hearts, there is only three such cards in the deck.

Therefore $P($heart face cards for two draws$)={3\over 52} \times {2\over 51}$.

• oops I totally knew that.. :) thank you! – Jessica Oct 9 '13 at 3:55

The number of cards that are Face cards AND Heart are = 3
Hence Probability $$P={3\over52}.{2\over51}$$

• how did you get 4? there are only 3 face cards that are hearts.. – Jessica Oct 9 '13 at 3:54