Let b and g represents the boy and the girl child respectively.

Now if a family has two children, the sample space will be

S = {(b, b), (b, g), (g, b), (g, g)}, n(S)=4

Let A be the event that both children are girls, the

A= {(g, g)}, n(A)=1

So the probability that both children are girls is

If the youngest is a girl

Let B be the event that the youngest child is a girl

Then B = {(b, g), (g, g)}, n(B) = 2

And the corresponding probability becomes

The sample space for the both girls is girl child and the youngest is a girl will become

(A∩B) = {(g, g)}, n(A∩B)=1

And the corresponding probability becomes

So the conditional probability that both are girls given that the youngest is a girl is