# Probability of a family having 3 girls and then a boy?

Helping my daughter with a science fair project.

We are a family with four kids, three girls and then a boy.

What is the probability of a family having four kids and the first three are girls and then a boy? So... want probability of four kids in that gender order - girl, girl, girl and then boy.

Thank you!

• Well I'd assume just (1/2)^4 = 1/16 Feb 21 '15 at 3:47
• i thought we'd proved prob(girl)=0.51?
– JMP
Feb 21 '15 at 3:59
• The answer is probably society-dependent. Whether people choose to have another child after say the second or third could depend on the sex distribution of the first couple of children. Feb 21 '15 at 3:59
• Oh, I never thought of it that way André. Feb 21 '15 at 4:03
• André raises another question, how many kids would one expect to need to have to get one of each gender? Feb 21 '15 at 4:53

The probabability of any combination in which the order is given is $\frac{1}{16}$.
We must have the events $G,G,G,B$ in that order where the probability of each one is $\frac{1}{2}$. Thus the probability is:
$\frac{1}{2}\times\frac{1}{2}\times \frac{1}{2}\times\frac{1}{2}=\frac{1}{16}$