A family has two children. What is the probability that both are girls, given that at least one is a girl?

Answer: 1/3

Explanation:

Here are all of the ways to list the sample space. B = boy, G = girl

BB

BG

GB

GG

We see that there are 3 cases in which there is at least one girl in the family. There is only one case where we have both children being girls. So the probability is 1/3.

In other words, we don't focus on the case BB since we know that at least one child is a girl, so we just focus on {BG, GB, GG}, and we note that GG only happens once out of the three possibilities.