We assume P(b)=P(g)=0.5.

Then the number of boys in a family of is a random variable with a binomial distribution with and .

So:

Alternatively consider all the families with children of whom are boys in birth order:

bbbg

bbgb

bgbb

gbbb

These are all equally likely, as are all families, so there are families with boys out of a total of possible families, so teh required probability is: