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A Positive Doesn't Always Mean Yes

🧪 You test positive on a 99%-accurate test. What is the chance it is real? Line up ten thousand people and the answer appears — if 1 person in 1,000 has it, then 10 of the 10 real cases test positive, and 100 of the 9,990 clear people test positive too. That is 110 positives in all, of which only 10 are real: 9%. There are so many clear people that the false positives swamp the real ones. 📉 Second, the curve. Without touching the test at all, changing only «how rare it is» moves the answer from 9% to 92%. Meanwhile raising «the share of true cases caught» from 80% to 100% barely moves it — what decides the answer is not the test but the rarity. 📬 Third, spotting it. With three tests that are all equally 99% accurate, 1-in-1,000, 1-in-100 and 1-in-10 give 9%, 50% and 92%. This app was made with code too · Remix it with the numbers of a test you know.