Question

Two cards are randomly chosen from a standard deck of 52 playing cards without replacement. What is the probability both cards will be hearts?

Answer 1

`3/51`

Explanation:

There are 52 cards in the deck, and 4 different suits:
Hearts, Clubs, Spades, and Diamonds.
Hence there are 13 cards of each suit.

So the probability of the first card being a heart is `13/52=1/4`

The cards are not replaced. Now there are 12 hearts in the deck, and 51 cards altogether.

So the probability of the second card being a heart is `12/51`

To find the probability of both of these events occurring, we multiply the probabilities together.

`1/4*12/51=3/51`