This is a great introduction to Bayes' Theorem and strong evidence that a large majority of medical doctors are not scientists.

About 85% of doctors get this problem wrong!

1% of women at age forty who participate in routine screening have breast cancer. 80% of women with breast cancer will get positive mammographies. 9.6% of women without breast cancer will also get positive mammographies. A woman in this age group had a positive mammography in a routine screening. What is the probability that she actually has breast cancer?

http://www.yudkowsky.net/rational/bayes