SCIENTIFICAMERICAN  |  Math

The false positive paradox explains why you misjudge risk

虚假阳性悖论解释了你为何误判风险

Isotype-inspired figures: one of a farmer and one of a librarian (to be assembled into a lineup of 11 of the farmer icons repeated, and one librarian.)

Isotype-inspired figures: one of a farmer and one of a librarian (to be assembled into a lineup of 11 of the farmer icons repeated, and one librarian.)

2026-03-17  1012  晦涩
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Puzzle number two gets more quantitative. Let’s say a doctor randomly decides to administer a blood test on you to scan for a certain disease that affects one in 1,000 people. The test is remarkably effective: it never gives a false negative, which means that if you have the disease, the test will detect it. False positives can happen but are rare: if you don’t have the disease, the test will say as much 99 percent of the time. Your test comes back positive. With these rates in mind, what is the probability that you have the disease? After the Steve example, you might have your guard up, ready for a trick. Try to inhabit the situation. You just got a positive result on an exceptionally accurate medical test. How worried do you feel?

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