I’ll come back to your reply later, but I would appreciate it if you could give a precise answer to the questions I asked.
It may help to find a common understanding on top of which we can build a clear discussion of the subtleties involved.
I don’t understand your point.
Wouldn’t you say that the answer to the following two questions is the same?
I tell you I have two children and that (at least) one of them is a boy, and ask you what you think is the probability…
…that I have two boys.
…that I have two boys or two girls.
In the first two cases, "single-sex" means "the same specific sex as the child you know the sex of" whereas in the last case it means "the same sex as a child that can still have two possible sexes".
If you would say,
> I tell you I have two children and that I’ve just sent you an email with the sex of (at least) one of them, and ask you what you think is the probability that the pair are both girls?
and then follow up with another question,
> what you think is the probability that the pair are both boys?
and then add the two probabilities up equally weighted, you might see why 1/2 is the reasonable answer in that case.
(And why opening up the email in question would reduce the probability of one of the questions to 0, and the other to 1/3.)