In culture A parents have children until they have a boy and

In culture A, parents have children until they have a boy and a girl (not necessarily in that order). In culture B, parents have children until they have 2 boys, regardless of the number of girls. Assuming children are born one at a time, that boys and girls are equally probable, and that families can have as many children until they decide to stop, calculate

a.) the expected number of children a culture A family will have

b.) the expected number of children a culture B family will have (hint: condition on the sex of the first child born)

c.) what is the expected number of boys and girls in each case?

Solution