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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

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