Update with the base rate

The idea

A conditional probability depends on what is already known. Evidence should change a starting assessment in proportion to how differently the evidence would occur under competing explanations. Rare possibilities can remain relatively rare even after an apparently impressive signal.

Worked example

Imagine 1,000 parcels, of which 10 contain a damaged item. A hypothetical scanner flags all 10 damaged parcels and also flags 99 undamaged parcels. There are 109 flags, but only 10 identify damage: about nine percent. A flag is useful because damage was only one percent before scanning, yet a flag is far from proof. The warehouse uses a second inspection rather than discarding every flagged parcel.

Use it carefully

This example uses invented, fixed error rates and a known prevalence. Real error rates can change with packaging and operating conditions. Conditional reasoning should not produce false precision when inputs are uncertain. Write a frequency table before calculating. For consequential screening, compare downstream harms and benefits, obtain domain expertise, and check whether additional evidence is independent of the first signal.

RETRIEVE. REASON. REMEMBER.

Knowledge check.

Choose one answer for each question, then check your reasoning.