Bayes' Theorem and Cancer Screening

If you get a positive result on a mammogram, what is the chance that you actually have cancer?

This video explains how Bayes' theorem can be used to answer this question. (Note: you will still have to do some research to get the exact rate of false negatives, rate of false positives, and rate of people in your age range who have cancer. But the numbers used in the video are approximately correct and the results are very revealing, both about Bayes' theorem and about cancer tests.)

And here is Julia Galef explaining how Bayes' theorem has changed the way she things in everyday life.