Medical Test Interpreter

Pre-Algebra · Axiom Academy

A test is "95% accurate" and yours comes back positive. The chance you're actually sick isn't 95% — it's closer to 1 in 6. Here's why. Picture 1,000 people and a disease that affects 1% of the population — its prevalence . Before anyone is tested, the truth is already fixed: a handful are genuinely sick, and almost everyone is healthy. Actually sick — about 10 people Actually healthy — about 990 people 2. Where the False Alarms Come From The test is 95% accurate in both directions: if you're sick it flags you 95% of the time, and if you're healthy it clears you 95% of the time. So it's wrong about 5% of the time — and that 5% is applied to both groups. 95% test positive correctly → about 9.5 true positives . 5% test positive by mistake → about 49.5 false positives . A small slice of a huge group can still outnumber a large slice of a tiny one. About 49.5 false alarms versus only 9.5 real cases — over five to one. The test almost never makes a mistake on any single person. But because there are so many healthy people, even a 5% error rate produces a crowd of false positives — far more than the disease itself produces. 3. What a Positive Result Really Means Now gather everyone who tested positive — the real cases and the false alarms together — and ask the only question that matters to you: among the positives, what fraction are actually sick? The total positives: about 9.5 + 49.5 = 59 people see a positive result.

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