5.18 Each child in Romania is equally likely to be a boy or a girl, independent of any other children.

a) Suppose we know that a family has n children. Show that the expected number of boys is equal to the expected number of girls. Did you need the assumption of independence?

b) Now suppose that, in addition of knowing that the family has n children, we also know that one of them is a boy (n > 1). Is it still true that the expected number of boys equals the expected number of girls? What happens if the assumption of independence is dropped?