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

#1**+2 **

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