Question

A family has two children. What is the probability that both the children are boys given that of them is a boy.

Answer 1

$P\left(\frac{B}{A}\right)=\frac{P(A\cap B}{P\left(A\right)}$

Sample space $S=\{MM,MF,FF,FM\}$

Both will be boys

$A:$ Event both children are boys.

$B:$ Event that at least one is big

$P\left(A\right)=\frac{1}{4},P\left(B\right)=\frac{3}{4},P(A\cap B)=\frac{1}{4}$

$P\left(\frac{B}{A}\right)=\frac{P(A\cap B)}{P\left(A\right)}=\frac{\frac{1}{4}}{\frac{3}{7}}=\frac{1}{3}$