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Two cards are drawn at random from a standard deck of 52 cards. What is the probability that they have the same rank?

rohitaop  May 31, 2018
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First we need to figure out how many ways to draw two cards from a standard deck of 52 cards.

To do this, we get: $$\binom{52}{2}=1326$$

The ways to chose them so their rank is the same is harder.

There are 13 different ranks, and in each rank, their are 4 suits.

To choose two cards in a rank, we have $$\binom42=6$$ ways to do this.

Since there are 13 ranks, we have: $$13\cdot6$$ ways to chose the cards so their rank is the same.

The probabilty is then $$\frac{78}{1326}=\frac1{17}$$

I hope this helped,

Gavin.

GYanggg  Jun 1, 2018
edited by GYanggg  Jun 1, 2018