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Originally Posted by Alan Anderson
You're missing the fact that there are two different ways in which the door may be answered by a two-girl family. Your analysis is looking at the probability of a girl answering, which doesn't matter for this problem, because a girl answering is given.
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Actually, I'm the only one catching it - it's twice as likely that a girl will initally answer from a G/G family than from a B/G family, and there are twice as many B/G families. Therefore, the other sibling has a 50/50 shot of being girly.