Can someone help me prove the following? For any events A, B, C with P(C) > 0: P(A union B | C) = P(A | C) + P(B | C) - P(A intersection B | C) Any help is appreciated. Thank you.
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Originally Posted by tshare1 For any events A, B, C with P(C) > 0: P(A union B | C) = P(A | C) + P(B | C) - P(A intersection B | C) $\displaystyle (A\cup B)\cap C=(A\cap C)\cup (B\cap C)$ Therefore $\displaystyle P[(A\cup B)\cap C]=P(A\cap C)+P(B\cap C)-P(A\cap B\cap C)$
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