Suppose 10 percent of the population has a disease. Everyone is tested, and your test comes back positive. The test is 80 percent accurate. What is the chance that you have the disease?

Surprisingly, it’s little more than 30 percent. If the population is 100, then 10 people have the disease. Eight of them will get a correct positive result, 2 will get a false negative, and 18 of the remaining 90 will get a false positive. That’s 26 positives, of which only 8 are correct, or 30.8 percent.