You draw two cards from a standard deck without replacement. What is the probability of drawing two hearts?

In a standard deck, there are 52 cards including 13 hearts.

The number of ways of drawing 2 cards from a deck of 52 cards
= C(52, 2)
= 52! / (50! 2!)
= 1326

The number of ways of drawing 2 cards from the 13 hearts
= C(13, 2)
= 13! / (11! 2!)
= 78

P(drawing 2 hearts from a deck)
= 78/1326
= 1/17

There are 13 hearts in a deck of 52 cards.

So the probability of the first card being a heart is (13/52) or (1/4).

After the first heart is drawn, there are 12 hearts left out of 51 cards. So the probability of another heart is (12/51)

Probability of both happening is the product of the individual probabilities:

(1/4)(12/51)
(1/1)(3/51)
1/17 or 0.0588

1 in 16