There are two possible ways of having two children (first second): MM MF FM FF. If he says one is a boy, that eliminates FF, so there are only three possible combinations remaining: MM MF FM. Of these, two have girls as the other child, so the chance is 2/3. (The answer to the supplementary question is 1/2, as expected, since the only remaining combinations after the first sentence are MM and MF, and the other one is a girl in 1/2 of them.)
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