Two cards are drawn at random from a standard deck of 52 cards, without replacement. What is the probability that both cards drawn are hearts?

1 Answer
Jul 26, 2016

The probability that both cards that are drawn are hearts is #1/17#.


First off, know that there are 13 heart cards in the deck of 52 cards. Therefore, the chance of pulling a single heart card is #13/52#. Let's say we do pull a heart card. Since there is no replacement for the heart card taken out of the deck, we now have 12 heart cards out a deck of 51 cards. The chance of pulling out a heart card in now #12/51#. To find the probability that both cards drawn out are hearts, multiply the two fractions together: #(13/52)*(12/51)=156/2652=1/17#.