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

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,



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

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