Mathematics
Bayes' Theorem and the Problem of False Positives
Quick fact
When a disease affects 1 in 1,000 people and the test is 99% accurate, a positive result means only about 9% of those who test positive actually have the disease—the other 91% are false positives. This is called the false positive paradox.
Why this is interesting
Imagine you test positive for a rare disease that affects only 1% of people. The test is 99% accurate. Would you assume you are 99% likely to have the disease? You might be surprised to learn the real probability is only about 50%.