What is the probability that a couple's first or second child will be a boy?

What is the probability that a couple's first or second child will be a boy?

• A. 1/2
• B. 1/4
• C. 3/4
• D. 1/3

Answer: (A)

Think about two independent births where each child is equally likely to be a boy or a girl. The four possible gender pairs for the two children are: boy–boy, boy–girl, girl–boy, and girl–girl. Each pair is equally likely. The event “the first or second child is a boy” means at least one of the two children is a boy. That happens in all cases except girl–girl. So three out of the four possible outcomes satisfy the event, giving a probability of 3/4 (0.75). If you were instead asked for exactly one boy among the two children, that would be two favorable outcomes (boy–girl and girl–boy), so 2/4 = 1/2.

Think about two independent births where each child is equally likely to be a boy or a girl. The four possible gender pairs for the two children are: boy–boy, boy–girl, girl–boy, and girl–girl. Each pair is equally likely.

The event “the first or second child is a boy” means at least one of the two children is a boy. That happens in all cases except girl–girl. So three out of the four possible outcomes satisfy the event, giving a probability of 3/4 (0.75).

If you were instead asked for exactly one boy among the two children, that would be two favorable outcomes (boy–girl and girl–boy), so 2/4 = 1/2.