Conditional probability and rare events
Randomness does not only deceive on small samples. There is a trickier trap: even a very accurate test for a rare disease produces a flood of false positives. Let's see why โ this is conditional probability.
Take a disease that affects 1 person in 100, and a test that is 90% accurate. The test comes back positive for some people. The bar shows everyone whose test fired: teal โ actually sick, yellow โ healthy people with a false positive.
Why this matters
This trap is real in medicine: when screening for rare diseases, most positive results turn out false, so the first test is followed by a confirmatory, more precise one.
The same effect drives fraud and spam filters: if fraud is rare, even a good detector will bury you in false positives unless the base rate is taken into account.
Where it shows up
Breathalyzers, lie detectors, "suspicious person" recognition in crowds โ all suffer from this: with a rare event and good accuracy, the absolute number of false positives is huge.
A competent conclusion therefore always weighs not only "how accurate is the test" but also "how rare is the event itself".