Quote:
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Originally Posted by Kris Verdeyen
PROBABLILITY THAT A GIRL WILL ANSWER...
...and the family has two boys - 0%
...and there's a boy and a girl - 25%
...and the family has two girls - 25%
So, a girl will answer (0% + 25% + 25%) = 50% of the time.
Exactly half of those responses will come from families with two girls, and exactly half will come from families with a boy and a girl.
Or I could be completely off base - let me know.
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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.