Back to Independence Now we can better understand independence using Bayes's Theorem. Eqn. 1.4 is particularly simple when A and B are independent. In this case the probability of B given A , $P(B\vert A)$ is just $P(B)$ because the probability of B is independent of the value of A . That's the whole definition of independence. So in that case we have $P(AB) = P(A)P(B)$.