Question

A couple has two children, one of which is a boy. What is the probability that they have two boys?

• A. $\frac{1}{2}$
• B. $\frac{2}{3}$
• C. $\frac{1}{3}$
• D. None of these

Answer 1

The correct option is C $\frac{1}{3}$

The sample space is (and needs to be) {BB,BG,GB,GG}.,

We know one child is a boys, so that rules out GG.

the probability that they have two boys $P\left(E\right)=\frac{1}{3}$