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The problem with that example is that there is no reason to assume that coat wearing and rain are independent (in fact, you have even modeled that wearing a coat is partially dependent on it raining).

Maybe I missed your point?



No, you're right those events shouldn't be called independent!

A defintition of independent events is:

    A and B are independent events iff P(A|B) = P(A) and P(B|A) = P(B)
So that was just plain wrong.




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