It is given that Mr. Smith has two children, so the different combinations of having two children are BB, BG, GB, and GG, all of which have equal probability, 1/4. It is also given that there is at least one boy. Therefore, we can cross out the GG combination. That leaves us with three combinations, BB, BG, and GB, all of which have equal probability, 1/3. Given that there is at least one boy, what is the probability that the other is a boy? Only one in the three combinations has two boys, therefore, the probability that the other is a boy is 1/3.
