Probability Intuition
Bayes' Theorem: The Medical Test
9 min+80 XPStep 1/10
The test that 'lies'
A disease affects 1 in 1,000 people. A test is 99% accurate: it catches 99% of cases and correctly clears 99% of healthy people. You test positive. How likely are you sick?
Almost everyone — doctors included — guesses ~99%. Watch what actually happens in a town of 100,000:
- Sick: ~100 people → the test flags ~99 of them
- Healthy: ~99,900 → the test still flags ~999 of them (1% false alarms)
Total positives: ~1,098. Actually sick: ~99. Your real odds: about 9%.
insight
A rare disease plus an imperfect test means most positives are false alarms. The base rate swamps the test's accuracy.