rates
Base rate fallacy
The test is accurate. The condition is rare. The name for that mix-up is the base rate fallacy.
The test is accurate, and the condition is rare. Of the alarms, how many are real?
Positive tests in this crowd, real ones first
Lock a guess, then draw the crowd. Green rings are real alarms. Coral rings are false alarms.
Almost everyone is well, so a small false-alarm rate still flags many healthy people.
The same accuracy applies to sick people and to well people. Sick people are scarce, so most of the alarms come from the well group.
A positive test is more believable when the condition is common, and less believable when it is rare.
A rare crime. A match that is rare among innocent people can still turn up several times in a large city.
A door and a test. Monty showing a goat and a positive test both leave you to count everyone that result fits.