Question

If the probability of A given B is 0.8 and the probability of A is 0.12 what is the probability of B

Answer 1

We can't tell from the information given. What we do know is

P(A ∩ B) = P(A|B) P(B)

We're given the conditional probability but not the probability of the conjunction.

If we were told P(A|B)=0.8 and P(A ∩ B)=0.12 we could conclude

P(B)=P(A ∩ B)/P(A|B) = 0.12/0.8 = 0.15

but that wasn't the problem asked.