Feh - again the correct answer relies on interpretation of the question. He phrased the question in a muddy way, then ignored the resulting uncertainty.
His phrasing (the setup):
“Let’s say, hypothetically speaking, you met someone who told you they had two children, and one of them is a girl.”
There are at least three possible ways to interpret this statement. If I heard the above in a random conversation (not some riddle thread on QT3), I would take it to mean “one of them is a girl [and the other is a boy]”, thus implying high confidence that the second is a boy.
But then, there is the follow up question/problem:
“What are the odds that person has a boy and a girl?”
OK, now we’re talking about a goofy riddle/problem. The follow up question implies that the first interpretation is probably not correct in this (contrived) context. But it still leaves open two possibilities.
The original statement could be interpreted as (and more precisely rendered as):
“…they had two children, and AT LEAST one of them is a girl.”
in which case the odds of one girl, one boy are 2/3.
or, it could be:
“…they had two children, and one identifiable one is a girl” (the older one, say, or the one known to the speker is a girl, and the other one is unknown), in which case the odds are probably around 50/50, but in context could actually be different. i.e. If it is known that the person has an 8 year old and a 9 year old, and you meet the parent at a ballet class where the 9 year old (a girl) is enrolled, but the 8 year old is nowhere in sight, it’s a reasonable inference that the chances that the 8 year old is a boy are >50%, since if both were girls, it would be likely that they would both be in the ballet class or at least the other one would be hanging around while the other is in class.
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So, again, we have a riddle where the asker tries to be clever, but in fact, provides insufficient information for a correct answer, and reasonable people can make different inferences from the question, resulting in different “correct” answers.
