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Notes on probability, panic & better guesses
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File 03Probability

The Base-Rate Machine

Why a positive test usually isn't.

Drag two sliders — how common a thing is, and how accurate the test is — and watch most “positive” results turn out to be false alarms. The rarer the thing, the more a single alarm lies to you.

Interactivethe base-rate machinedrag the sliders

Before the test

4%

the base rate

After a positive

29%

chance it's real

Out of 100, 14 come back positive — but only 4 are actually the real thing.

A 90%-accurate test moved you from 4% to 29% — a real update, but a “positive” is still more likely a false alarm than the real thing. The rarer the thing, the more a single alarm lies.

Works for anything that flags rare things: medical screens, spam filters, fraud alerts, lie detectors. “Accurate” is one number standing in for both sides — how often the test is right when it isthe real thing, and when it isn't.

  • real & flagged
  • false alarm
  • real, missed
  • correctly clear