Question

assume that boys and girls are equally likely. find the probability that when a couple has three children, there are exactly 3 girls. what is the probability of exactly 3 girls out of three children? (type an integer or a simplified fraction.)

Explanation:

Step1: Determine probability of one - child event

The probability of having a girl for each child is $\frac{1}{2}$ since boys and girls are equally likely.

Step2: Use multiplication rule for independent events

Since the gender of each child is an independent event, for 3 children, the probability of having a girl each time is $P=\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}$.

Step3: Calculate the result

$P = \frac{1\times1\times1}{2\times2\times2}=\frac{1}{8}$.

Answer:

$\frac{1}{8}$