Science Puzzle
The Base Rate Fallacy
A disease affects 1 person in every 10,000. A test for the disease is 99% accurate, meaning it correctly identifies 99% of people who have it and correctly clears 99% of people who do not.
You take the test and it comes back positive. What is the probability that you actually have the disease?
The Answer
About 1%, not 99%. The test accuracy feels like it should translate directly into the probability of being ill, but it does not, because the disease is extremely rare.
In a population of 10,000, only 1 person has the disease. The test finds that person correctly (1 true positive). But the test also wrongly flags 1% of the 9,999 healthy people, which is about 100 false positives. So among all the positive results, roughly 101 in total, only 1 person is actually ill. That is a chance of about 1 in 100, not 99 in 100.
This is the base rate fallacy. When a condition is very rare, even an accurate test produces many more false alarms than correct detections. The base rate, how common the thing is in the first place, must always be factored in alongside the test accuracy.
The principle: The base rate fallacy. Even a highly accurate test produces far more false positives than true ones when the condition being tested for is very rare. The rarity must be factored in.