8.

(a) Suppose you flip two independent fair coins. If at least one head results, what is the probability of two heads?

(b) Suppose the sexes of children in a family are independent, and that boys and girls are equally likely. If a family with two children has at least one girl, what is the probability they have two girls?

(c) Again suppose the sexes of children in a family are independent and that boys and girls are equally likely. Imagine a family with two children who are not twins. Suppose that the older child is a girl. What is the probability that they have two girls?