Bayes's Theorem Again you have your two events A and B but they no longer need to be independent. Then you can say the following $$P(AB) = P(A)P(B\vert A).$$ (1.4) What's the meaning of this? $P(B\vert A)$ means "the probability of B given A". It's called a "conditional probability". So this says the probability of having both A and B is (the probability of A) times (the probability of B given you've also got A). Although this might seem unintuitive, it's pretty simple if you think about it using Venn diagrams we just talked about. Let's try to understand the case of two intersecting circles. What's $P(B\vert A)$? That is the probability of B given A. In terms of darts, this means that we're assuming that your dart fell inside circle A . What fraction of those darts were also inside B ? Well, that's just just the area of $AB$ divided by the area of A , that is $P(B\vert A) = P(AB)/P(A)$. Hey that's just a rearrangement of Bayes's Theorem, eqn 1.4.