SciAm on Bayes’ theorem
Scientific American expands on Bayes’ theorem with a simple riddle:
A patient goes to see a doctor. The doctor performs a test with 99 percent reliability - that is, 99 percent of people who are sick test positive and 99 percent of the healthy people test negative. The doctor knows that only 1 percent of the people in the country are sick. Now the question is: if the patient tests positive, what are the chances the patient is sick? The intuitive answer is 99 percent, but the correct answer is 50 percent, and Bayes’s theorem gives us the relationship between what we know and what we want to know in this problem.
Bayesian probability is another interesting read from Wikipedia.