G.

Bayes' Theorem You Can See A probability is a share of the dots. P(A) is the part of the box covered by circle A, and P(B given A) is the part of A that is also in B: the lens divided by A. Slide the circles around and every number updates: apart, the lens is empty and both conditionals are 0; tuck B inside A and P(A given B) becomes 1. The lens is the same in both directions, so P(B given A) P(A) = P(A given B) P(B) and dividing gives Bayes' theorem: P(B given A) = P(B) P(A given B) / P(A) P(A given B) = P(A) P(B given A) / P(B) The bottom box computes each one from the other side, live, and it always lands on the same number as the picture above.