Bayes' theorem
Frequentist interpretation

In the frequentist interpretation, probability measures a "proportion of outcomes". For example, suppose an experiment is performed many times. P (A) is the proportion of outcomes with property A (the prior) and P (B) is the proportion with property B. P (B | A) is the proportion of outcomes with property B out of outcomes with property A, and P (A | B) is the proportion of those with A out of those with B (the posterior).

The role of Bayes' theorem is best visualized with tree diagrams. The two diagrams partition the same outcomes by A and B in opposite orders, to obtain the inverse probabilities. Bayes' theorem links the different partitionings.
combination:two_responses