On a Friday afternoon in 1989, the physicist Leonard Mlodinow got a phone call from his doctor. His doctor told him there was an over 99 percent chance that he was infected with HIV.
The doctor was wrong. Not only was the physicist HIV-free, the chances that he was sick had really been less than 10 percent.
The doctor had done his medical testing perfectly. He just messed up the statistics.
In particular, he failed to use Bayes’s Theorem.