# Math Help - Conditional Probability Proof

1. ## Conditional Probability Proof

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.

2. 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)
$(A\cup B)\cap C=(A\cap C)\cup (B\cap C)$
Therefore $P[(A\cup B)\cap C]=P(A\cap C)+P(B\cap C)-P(A\cap B\cap C)$