Problem 52 Solution

Since the probability is 50/50 for a boy or girl in each pregnancy there are four possibilities for a two child pregnancy, each with equal probability:

  1. Boy then boy
  2. Boy then girl
  3. Girl then boy
  4. Girl then girl
We know that for this particular mother the last possibility is not the case. The other three are still equally likely. In two of the other possibilities the other child is a girl, in one it is a boy. Thus the probability that the other child is a boy is 1/3.

Note: This is similar to the question in problem 16 which approaches the solution another way.

Michael Shackleford, A.S.A.