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 as they like until they decide to stop, calculate (a) the expected number of children a Culture A family will have, and (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?
For part a , I get the expected number is 3. Is it correct? In my thinking that Let X be the number of children. And if the first child is boy or girl, then （X-1）~geom(1/2). Thus, E(X-1）=2. And E(X)=1+E(X-1)=1+2=3.
In part b I got the expected number is 4. So, part a and b is done.
For Part C the question ask boys and girls in each case?Does is mean I need to find 4 expected numbers , 1 for boys and 1 for girls in each case?