Question

Find the probability that when a couple has two children, at least one of them is a boy. (Assume that boys and girls are equally likely.) (Simplify your answer. Do not round.)

Answer 1

Finding the probability that when a couple has two children, at least one of them is a boy:

Given,

The boys and girls are equally likely. So $P\left(B\right)=\frac{1}{2};P\left(G\right)=\frac{1}{2};$

Let the couple have two children that is one one girl or two boys. [Since they have at least one boy]

Probability$=P\left(B\right)P\left(G\right)+P\left(B\right)P\left(B\right)$

$$\begin{gathered} =\left(\frac{1}{2}\right)\left(\frac{1}{2}\right)+\left(\frac{1}{2}\right)\left(\frac{1}{2}\right) \\ =\frac{1}{4}+\frac{1}{4} \\ =\frac{2}{4} \\ =\frac{1}{2} \\ =0.5 \end{gathered}$$

Hence, the probability of the given condition is $0.5$.