  This instance of Bayes’ Theorem deals with the simple case where one has two hypotheses H and J that are mutually exclusive and jointly exhaustive, and where one is interested in \(\Pr(H \mid E)\), that is, the probability that H is true given evidence E. What this instance of Bayes’ Theorem does is provide one with a way of calculating that probability, provided that one knows, first of all, \(\Pr(H)\) and \(\Pr(J)\)—that is, the a priori logical probabilities of \(H\) and \(J\)—and also, second, \(\Pr(E \mid H)\) and \(\Pr(E \mid J)\)—that is, the logical probability of \(E\) given, respectively, only \(H\) and only \(J\).  By substitution in (1), we have: 