Question

Consider the composition of a 3-child family in which the children were born at different times but a girl is as likely as a boy at each birth. What is the probability that the oldest child and the youngest child are of the same gender?

Answer 1

Let's denote B for the birth of the boy and G for the birth of the girl.

There 8 possible outcomes:

BBB, BBG, BGB, GBB, BGG, GBG, GGB, GGG

The oldest child and the youngest child are of the same gender: BBB, BGB, GBG, GGG.

Therefore the probability that the oldest child and the youngest child are of the same gender is

$P = \cfrac{4} {8} = \cfrac{1} {2}.$