Probability Question - Prove Formula

AI Thread Summary
The discussion centers on proving the formula P(A∪B|C) = P(A|C) + P(B|C) - P(A∩B|C). The initial approach involves using the formula P(A∪B|C) = (P(A∪B)P(C|A∪B))/P(C), but the user struggles to progress from this point. It is noted that the user initially assumed independence among events A, B, and C, which led to confusion in solving the problem. Ultimately, the user realizes that the events may not be independent, which clarifies their understanding of the formula. The discussion highlights the importance of recognizing dependencies in probability problems.
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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
 

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