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.)
the probability is
(simplify your answer. do not round)

Explanation:

Step1: List all possible outcomes

The possible combinations of children for a couple with two - children are (boy, boy), (boy, girl), (girl, boy), (girl, girl). So, the total number of possible outcomes $n(S)=4$.

Step2: List the favorable outcomes

The favorable outcomes (at least one boy) are (boy, boy), (boy, girl), (girl, boy). So, the number of favorable outcomes $n(A)=3$.

Step3: Calculate the probability

The probability formula is $P(A)=\frac{n(A)}{n(S)}$. Substituting the values, we get $P(A)=\frac{3}{4}$.

Answer:

$\frac{3}{4}$