I'm new at Statistics and I was wondering some problem. Suppose you have two independent events $A$ and $B$ and you want to calculate the conditioned probability of having either $A$ or $B$ if you have $C$, that is: $P(A\cap B \mid C)$
Is this correct: $$P(A\cap B \mid C) = P(A \mid C) \cap P(B \mid C)\,\,?$$
Thanks a lot!