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I am trying to understand what's wrong with the following logic related to "multiple conditioning." Why is the probability of [(A given B) given C] not the same as the probability of [A given (B and C)] ? I know it's not true, but only because numbers disagree. I am having a hard time parsing what's wrong with the logic.

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    Both are the same thing. What numbers disagree?2011-12-18
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    There is no such thing as [A given B]. There is such a thing as the probability given B, of A.2011-12-19

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