Bill and Gates go target shooting together. Both shoot at a target at the same time. Suppose Bill hits the target with probability $0.7$ ,and gates independently hits the target with probability $0.4$. Given that target is hit, what is the probability Gates hit it?
I tried using: $$P(A\cup B)=P(A)+P(B)-P(A).P(B)$$ and the answer could be: $P(A\cup B)-P(B)$
Maybe Baye's theorem can be used?