If I choose four cards from a standard -card deck,with replacement, what is the probability that I will end up with four cards from the same suit?

Guest Apr 20, 2022

#1**0 **

The first card can be any suit so we don't need to include it into the calculation.

Because each card is replaced after it is drawn, there is a 1/4^{th} chance that the second card will match the first.

It is also true that the third card has a 1/4^{th} chance that it will match the first two.

Lastly, the fourth card has a 1/4^{th} chance that it will match the first three.

Multiplying together these possibilities, we get a probability of (1/4) x (1/4) x (1/4) = 1/64.

geno3141 Apr 20, 2022