Thomas Bayes (1701-1761) developed a mathematical rule that deals with calculating P[B/A] from information about P[A/B]. Bayes’ theorem states the following:
P[B’] = the probability of the complement of Event B
P[A/B’] = the probability of Event A, given that the complement to Event B has occurred
Now that looks like a mouthful, but applying it in our tennis example will clear things up. With Bayes’ theorem, we can calculate P[B/A], which is the probability that the warm-up was less than 10 minutes, given that Debbie won the match. Using the values from the previous figure:
Knowing that Debbie won the match, ...