SOLUTION: A family has two children.What is the probability that the younger child is a girl,given that at least one of the children is a girl?

This is a conditional probability problem:

Sample space =

{GG, GB, BG, BB}  where the first letter, G or B, represents the 
                  older and the second letter represents the younger.

Since we are given that at least one of the children is a girl, the
reduced sample space does not include BB.

Reduced sample space =

{GG, GB, BG}

The only successful ones are GG and BG.

That's 2 ways out of 3.

So the conditional probability is 2/3

Edwin