A family has two children, one is a boy, what are the odds the other is too?
Mr. Smith has two children, and at least one of them is a boy. What's the probability both children are boys? Most people confidently answer 1/2. Martin Gardner posed this exact puzzle in his 1959 Scientific American column, and the 'obvious' answer isn't so simple.
Reveal the answer
With no other information about how you learned that fact, the answer is 1/3, not 1/2, because among the equally likely combinations {boy-boy, boy-girl, girl-boy, girl-girl}, ruling out girl-girl leaves boy-boy as only one of three remaining options. Gardner himself later admitted the puzzle is genuinely ambiguous: the answer legitimately becomes 1/2 if the fact was revealed by, say, randomly picking one child and observing it's a boy, rather than merely being told 'at least one' is. First posed in Martin Gardner's 'Mathematical Games' column, Scientific American, May 1959.
— Martin Gardner, Mathematical Games column, Scientific American — May 1959