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This is embarrassing, but I am unable to prove that $P(A^c \cap B) = P(B) - P(A \cap B)$. Any pointers?

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    **Hint**: What is $(A^c \cap B) \cap (A \cap B)$? What is $A^c \cup A$? Moving the $P(A \cap B)$ term to the other side may make things *seem* clearer.2011-12-10
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    I'd have posted an answer, but "cardinal"'s comment says essentially what I would have said.2011-12-10
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    A different viewpoint (but basically the same thing as the above comments): Do you know that $B=(A^c\cap B) \cup (A\cap B)$ and the set $(A^c\cap B)$ and $(A\cap B)$ are disjoint? What do you know about probability of union of disjoint events?2011-12-10
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    @MichaelHardy: You (or others) should feel free to post an answer. Cheers. :)2011-12-10
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    @PKR: For future reference in asking homework questions, many users will generally want to see some attempt at a solution or more developed reasoning explaining why and where you are stuck. There is a helpful [homework FAQ](http://meta.math.stackexchange.com/questions/1803/how-to-ask-a-homework-question) that I'd encourage you to read over. Cheers.2011-12-10

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