Why a Positive Test Is Usually a False Alarm (for Rare Conditions)
You test positive on a 99% accurate test. Are you sick? Using a grid of 10,000 people, we see that for a 1-in-1,000 condition, about 100 healthy people get flagged versus about 10 real cases, so only about 9% of positives are real.
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The prompt
Made in the educationalaivideos Studio. Topic: Why most positive results for a rare condition are false positives: 1 in 1,000 people have it, the test catches 99% of real cases and wrongly flags 1% of healthy people, so only about 9% of positives are real. Audience: Curious general audience scrolling short videos; no maths background Length: 1m, vertical Notes: Open with the hook: You test positive. 99% accurate test. Are you sick? Use a grid of dots for 10,000 people.
Transcript
You test positive. The test is ninety-nine percent accurate. Are you sick? Probably not. Here's why. Picture ten thousand people. The condition is rare: one in a thousand people have it. That's just ten of these dots. The test catches ninety-nine percent of real cases, so nearly all ten test positive. But it also wrongly flags one percent of healthy people. One percent sounds tiny, but there are nine thousand, nine hundred and ninety healthy people. That's about a hundred false alarms. Now gather everyone who tested positive. About a hundred and ten people. Only ten of them are actually sick. Ten out of a hundred and ten is about nine percent. So your positive result means roughly a one in eleven chance you're sick. When a condition is rare, false alarms from the huge healthy crowd outnumber the real cases. That's why a positive result is usually confirmed with a second test.
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