In a certain village, it is traditional for the eldest son (or the older son in a two-son family) and his wife to be responsible for taking care of his parents as they age. In recent years, however, the women of this village, not wanting that responsibility, have not looked favorably upon marrying an eldest son.
(a) If every family in the village has two children, what proportion of all sons are older sons?
(b) If every family in the village has three children, what proportion of all sons are eldest sons?
Assume that each child is, independently, equally likely to be either a boy or a girl.