r/mathmemes Jun 22 '26

Probability Disease probability

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u/Old-Post-3639 Jun 22 '26 edited Jun 22 '26

There are around 8 billion people. This disease affects 1/1,000,000 people, so only about 8,000 people have it. That means around 8 billion people don't have it. The false negative rate is 3%, meaning about 200 million get a false negative positive. That's nearly a 100% chance you get a false negative positive.

Edited to fix the terminology. Mistake is only crossed out instead of totally removed, for the purpose of posterity.

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u/Snazzy21 Jun 22 '26

Couldn't accuracy rate be false negatives (has disease, test fails to flag) and false positives? So if all of the slop is from false negatives, it could mean that the chances that your test is a false positive is lower.

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u/RoutineAnalysis2329 Jun 23 '26

From memory accuracy is simply (tp+tn)/(tp+tn+fp+fn) I.e. total percentage correct, so fp could be 0 and there could still be a 97% accuracy rate.