Thanks for the clarification, though I think my point stands. > The way the puzzle is phrased, the only way to get 1/3 as an answer is to assume that parents w

Thanks for the clarification, though I think my point stands. > The way the puzzle is phrased, the only way to get 1/3 as an answer is to assume that parents with one girl will never say, "At least one of them is a girl." Right. But that is assumed, because the puzzle states that the parent says, "At least one of them is a boy." In other words, "Put this way, the puzzle is highly ambiguous." No, not it is not. It is absolutely not ambiguous. I made this point in a different comment for a different blog post with the same example, but: both things you link to contain a fallacy, as follows. "Suppose we know that a certain man has two children and we also know that the older one is a boy" IMPLIES "Now suppose we know simply that a man has two children and that one of them is a son. This time we would reason that there is no possibility that the person has two girls. It follows that the sexes of his two children, ordered from oldest to youngest, are either BB, BG or GB...." You can't conclude, as these authors do, from the first case, that the other child's gender is 1/2, and from the second, it is 1/3. It's not that the two cases are different (in any important way); they are not; one implies the other. It's that in the 1/2 case, the person is naive, and in the 1/3 case, the person takes into account the known fact that there is a 1/2 chance per child of getting a certain gender, thus allowing the BB/BG/GB/GG analysis.