Ignoring the Base Rate

Our minds latch onto a vivid number and forget how common the thing was to begin with. A test that is 99% accurate sounds nearly perfect. But if a disease affects only 1 in 10,000 people, most positive results will still be false alarms, because there are so many more healthy people to misflag than sick people to catch. The accuracy figure is real; the conclusion most people draw from it is wrong. Always ask how rare the underlying event is before you trust what a number seems to imply.