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

1 Answer

Jan 3, 2016

$\frac{3}{51}$ $3/51$

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 $\frac{13}{52} = \frac{1}{4}$ $13/52=1/4$

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 $\frac{12}{51}$ $12/51$

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

$\frac{1}{4} \cdot \frac{12}{51} = \frac{3}{51}$ $1/4*12/51=3/51$

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