Reckoning With Risk, by Gerd Gigerenzer

The test for breast cancer is extremely reliable. It correctly detects breast cancer in 90% of cases when the cancer does exist, and only mistakenly reports it in 9% of cases when the cancer doesn't exist. The incidence of breast cancer in women is 1 in 100. Suppose you (or, for men, a woman close to you) take a test for breast cancer, and unfortunately it returns a positive result (i.e. it detects the cancer). What is the probability that you do have breast cancer? Would you be surprised to know it's just 10%? Not 90%, 99% or some other high number?

Another example: DNA testing on a murder weapon matches your DNA, and a forensic expert says there's only a 1 in 100,000 chance of that happening. Are you doomed? Would you be surprised to know that in a city of, say, 2 million people, this means you're 95% likely to be NOT guilty, based on that DNA evidence alone?

Do these examples surprise and confuse you? If so, take heart: They surprise and confuse most people - laypeople and experts (doctors and lawyers) alike. Unfortunately, this can have disastrous - sometimes tragic - consequences in law, medicine and other fields.

This is the sort of confusion that occurs when experts don't know how to present complex information in a clear way. It's a pity, especially when there are ways to present this simply - without being simplistic. Gigerenzer shows you how.