Question

What is the probability of a family with 5 children having 4 girls

Answer 1

Let X denote number of girls in n=5 independent births, where each has a probability p=0.5.

We denote:

$$Binomial(n=5, p=0.5)$$

Probability of x number of girls is:

$$P(X=x)=n!/(x!(n-x)!)*p^x*(1-p)^{n-x}$$

Then the probability of a family with 5 children having 4 girls is

$$P(X=4)=5!/(4!(5-4)!)*0.5^4*(1-0.5)^{5-4}=0.15625=5/32$$