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:

where:

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, ...

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