i think it's like this.... interpretation 1.. we select a random FAMILY from the set of all families with two children.one of the children happens to be a boy.

i think it's like this.... interpretation 1.. we select a random FAMILY from the set of all families with two children.one of the children happens to be a boy. {BB, BG, GB} are possibilities. P(BB) = 1/3 interpretation 2.. we select a random CHILD from the set of all families with two children. one of the children happens to be a boy. in this case we have the following possible combinations [B1B2, G1B3, B4G2]. we know it's a boy, so what's the probability that B1 or B2 was selected? 1/4+1/4 = 1/2.