The analogy is deep. But actually the relationship is as follows: P(A u B) = P(A) + P(B) - P(A^B) P(A ^ B) = P(A u B) - P(A) - P(B) And to the guy who said x

The analogy is deep. But actually the relationship is as follows: P(A u B) = P(A) + P(B) - P(A^B) P(A ^ B) = P(A u B) - P(A) - P(B) And to the guy who said xor is addition — no it’s not: P(A xor B) = P(A) + P(B) - 2 * P(A^B) In Probability, when you have a space of outcomes, doing a Union on two disjoint events (sets of outcomes) the probabilities add. Whereas doing an Intersection on two non-disjoint events those probabilities multiply. If two events have no outcomes in common, for instance, the probability of them both occurring is zero. When you “condition” probability on an event X happening, you restrict the space of all outcomes to that set X, and intersect every event with it. When you condiition B[n] = A[n] given that (A[n-1] AND … A[1]) having already happened, you have a sales funnel and each step is independent of the previous, so the probabilities multiply. It is also called a Markov Chain if you have a discrete set of possibilities at each step so you can form a matrix.