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nshepperd comments on Bayes' Theorem Illustrated (My Way) - Less Wrong
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Flip two coins 1000 times, then count how many of those trials have at least one head (~750). Count how many of those trials have two heads (~250).
Flip two coins 1000 times, then count how many of those trials have the first flip be a head (~500). Count how many of those trials have two heads (~250).
By the way, these sorts of puzzles should really be expressed as a question-and-answer dialogue. Simply volunteering information leaves it ambiguous as to what you've actually learned ("would this person have equally likely said 'one of my children is a girl' if they had both a boy and girl?").
Yeah, probably the biggest thing I don't like about this particular question is that the answer depends entirely upon unstated assumptions, but at the same time it clearly illustrates how important it is to be specific.