Answer to Question #383 in Statistics and Probability for Jeana

Question

Consider a family with two children. What is the probability that both kids are boys if:
a) the elder child is a boy;
b) at least one child is a boy?

Answer 1

a) If a family has two children, there maybe 4 cases (older - younger): boy-boy, boy-girl, girl-boy, girl-girl. The last 2 of these 4 cases obviously can not happen. Thus, we are interested in one of the two remaining variants. Its probability is 1/2.

b) If a family has two children, there maybe 4 cases (older - younger): boy-boy, boy-girl, girl-boy, girl-girl. The last one of these 4 cases obviously can not happen. Thus, we are interested in one of the three remaining variants. Its probability is 1/3.