A family has three children. Denoting a boy by B and a girl by G, we can denote the genders of these children from oldest to youngest. For example, GBG means the oldest child is a girl, the middle child is a boy, and the youngest is a girl. There are eight possible outcomes: BBB, BBG, BGB, BGG, GBB, GBG, GGB, and GGG. Suppose these outcomes are equally likely.
What is the probability that the youngest child is a boy?
What is the probability that the oldest child and the youngest child are of the same gender?
What is the probability that the family has no boy?