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For the "two child problem":
A man has two children, the older is a son.
A woman has two children, one of which is a son
Which is more likely to have two sons?
There is one solution, not excluded by the statement of the problem, which
I do not recall having seen mentioned, viz: that the man and the woman are
married to each other and the children are their own. In which case the
answer is clear.