Probability Question - Prove Formula

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Homework Statement

Hi,

Prove P(AUB|C) = P(A|C)+P(B|C)-P(A∩B|C)

Homework Equations

The Attempt at a Solution

I start off from here

$P(AUB|C)=\frac{P(AUB)P(C|AUB)}{P(C)}$

I don't know where to go from here. Thanks for any help that you can provide.

 

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I think I actually figured this one. I realize that A, B, C may not necessairly be independent and for whatever reason I thought they where so I wasn't getting the correct answer