Test positive on a 99%-accurate test? You're probably still healthy.
The rarer the disease, the more a "positive" result lies. Guess the real odds, then play with the numbers yourself.
A test for a rare disease is 99% accurate. Only 1 in 1,000 people actually have the disease. You test positive. What's the chance you actually have it?
Play with the numbers
This is the base rate fallacy. "99% accurate" describes the test, not your odds. When a disease is rare, the huge pool of healthy people gives the test far more chances to be wrong about someone healthy (a false positive) than the tiny pool of sick people gives it chances to be right about someone sick (a true positive) — even at a 1% error rate.
The actual math is Bayes' theorem: your true odds after a positive result depend on both the test's accuracy and how common the condition is beforehand (the "base rate"). Ignore the base rate, and a genuinely accurate test can still leave you mostly wrong.
See also: the Monty Hall Problem and the Birthday Paradox, two more probability results that break most people's first instinct.
Source: Bayes' theorem (classical probability theory). Base-rate neglect as a documented cognitive bias: Kahneman & Tversky (1974); in medical-testing contexts specifically, Gigerenzer & Hoffrage (1995) found even practicing physicians routinely get this calculation wrong.