I know this has been answered a dozen times, and I know entirely how to get the 2 possible answers. My question revolves around the phrasing of this question, aren't (1) and (2) the exact same question?
A neighbor of yours has two children. Assuming that the gender of a child is like a coin flip, it is most likely that the neighbor has one boy and one girl, with probability of a half. The other possibilities are a quarter each (either two boys or two girls).
(1) Suppose that you ask the neighbor whether she has any boys, and she said yes. What is the probability that one child is a girl?
(2) Instead, suppose that you happened to see one of her children passing by, and it was a boy. What is the probability that the other child is a girl?
In both questions, it states that we have knowledge of the neighbor having a boy. The first question, she says yes (she has at least one boy). The second, we see at least one boy. Both asks the probability of the other child being a girl. Clearly, as I've read the other questions on this topic, as well as the wiki this is a play on words. So I guess I'm having trouble depicting which one is 2/3 and which is independent of each other and thus 1/2.