Consider a family that has two children. We are interested in the children's genders. Our sample space is S = {(G,G), (G,B), (B,G), (B,B)}. Also assume that all four possible outcomes are equally likely.

a. What is the probability that both children are girls given that the first child is  girl?

b. We ask the father: "Do you have at least one daughter?" He responds "Yes!" Given this extra information, what is the probability that both children are girls? In other words, what is the probability that both children are girls given that we know at least one of them is a girl?