For many problems involving conditional probability, Bayes’s theorem provides a divide-and-conquer strategy. If is hard to compute, or hard to measure experimentally, check whether it might be easier to compute the other terms in Bayes’s theorem, , and .

If the Monty Hall problem is your idea of fun, I have collected a number of similar problems in an article called “All your Bayes are belong to us,” which you can read at http://allendowney.blogspot.com/2011/10/all-your-bayes-are-belong-to-us.html.

[1] Based on an example from http://en.wikipedia.org/wiki/Bayes’_theorem that is no longer there.

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