This question is a variant of the Boy or Girl Paradox, which Wikipedia attributes to Martin Gardner. Wikipedia also writes that "the paradox has frequently stimulated a great deal of controversy"
Wikipedia calls this question a paradox, because:
On the one hand, the birth of a boy as the first child means nothing for the second child: the expecting parents should still give the probability of their next child being a boy as roughly 0.5 (I know that's not exact, just pretend for now).
On the other hand, the guy at the bar (or job interview) might look at the problem differently, because the events have already happened: we know that this parent has two children. What is the likelihood that both are boys vs. the likelihood that one is a boy and one is a girl? Put in that way, the likelihood of having two boys is lower than the likelihood of having children of two genders, because there are two possible states of affairs (out of 4) that would result in that outcome: first boy then girl, and first girl then boy.
In other words, the possible combination of genders for two children is: B/B ; B/G ; G/B ; G/G
The actual solution? It depends how the question is asked, or how and when you discover that one of the children is a boy. From the manner quoted here, the question is ambiguous. If the stranger offered this information to you upfront, than from your perspective, is it as if the stranger is offering information regarding a random child, in which case the answer would be 1/2, or specifically the child that is not the stranger him/herself? In the latter case, the answer would be 1/3, because your original sample size is only the families of two children where one of them is a boy, (or, in another version, you specifically ask, "is one of them a boy", not picking a child at random) and we want to know, of those families, what is the probability that the other child is also a boy.
Eliezer Yudkowsky (a relatively well-known AI researcher) has a lovely story about this problem where writes that an incorrect wording of it changed his life. He, and the linked Wikipedia article, both have good explanations to a Baysian analysis of the problem and its solution.
Of course, the questioner probably should have also stipulated that it's a way of asking a probability puzzle, so that there wouldn't be any demographic or sociological factors to consider. That way, you can discuss this as a case where boy:girl ratio is 1:1 and that the sex one child doesn't affect the probability of the sex of a second child (which technically isn't true, partly because there's a possibility that the two children are twins), etc. because after all, that's not really the exciting part of the puzzle, is it?