A family has two children. If the first child is a boy, find the probability that the other child is also a boy.

Let $B$ represent a boy and $G$ represent a girl. The sample space for two children is:
$$S=\{BB,BG,GB,GG\}$$
We are given the condition that the first child is a boy. This restricts the sample space to:
$$S^{\prime }=\{BB,BG\}$$
The event that the other child is also a boy corresponds to the outcome $\{BB\}$.Number of favorable outcomes $=1$ Total outcomes in the reduced sample space $=2$ $
$P=\frac{1}{2}$ $