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Probability
The boy or girl paradox
Martin Gardner, Scientific American, May 1959; in his October 1959 column he admitted the wording was ambiguous.
Treat every birth as a fair and independent coin toss: boy or girl, each with probability 1/2. Mr Smith has exactly two children. You know nothing else about them.
You ask him one question: 'Do you have at least one son?' He answers 'Yes', and you can take the answer as honest. Nothing about how you met him, or which child you might have seen, enters into it; all you have is his answer to that question. What is the probability that both of his children are boys?