The Deadly Disease Puzzler

This is one of the world's most significant puzzlers. This puzzler dramatically shows how easy it is to jump to a terribly wrong conclusion if you don't understand statistics. Furthermore, this is a realistic situation faced by thousands of people every year.

Your doctor gives you the bad news that you have tested positive for a deadly disease. The test is 99% reliable. Of people who actually have the disease, 99% test positive and only 1% test negative. Of people who don't have the disease, 99% test negative and only 1% test positive.

Unfortunately, you have tested positive. What is the probability that you have the disease? Or answer this simpler question: Are you likely to have the disease or not?

Think about it before looking at the answer.