 The Law of Total Probability basically says that we can calculate the probability of \(A\) by breaking it down into two possible cases: \(B\) and \(\neg B\). We consider how likely \(A\) is if \(B\) is true and how likely it is if \(B\) is false. We then give each case appropriate “weight”, by multiplying it against the probability that it holds, then adding together the results. For this to work, \(p(A\mid B)\) and \(p(A\mid \neg B)\) have to be well-defined, so \(p(B)\) can’t be 0 or 1.