We know two things:
0. The probability of obtaining a boy and a girl is the same.
,1. The gender of a child is independent of the gender of any brothers or sisters.
This means that each pregnancy has the same probability of obtaining boys or girls. Even if she have had three girls, the probability is the same for the fourth baby than for the first one.
This means that the probability of obtaining a girl when their fourth baby is born is 1/2.
