The Bayesian Trap - A Mathematical Case for Trying Something New

Humans are notoriously terrible at intuitive probability. Imagine you wake up feeling slightly off. You visit the doctor, and she runs a battery of tests. A week later, she calls with bad news: you tested positive for a rare disease that affects 0.1% of the population. Panicked, you ask how accurate the test is. "It correctly identifies 99% of people who have the disease," she says, "and only gives a false positive to 1% of healthy people." If you rely on your gut, you probably assume you have a 99% chance of being sick. But here's where the math kicks in. Most people latch onto one thing the doctor said — "99% accurate" — and conclude that a positive result means a 99% chance of illness. The human brain is terrible at remembering the prior when presented with shiny new evidence. We fixate on the test's accuracy and forget the other crucial piece of information: "...a rare disease that affects 0.1% of the population." So which is it — 0.1% or 99%? Neither. The true probability depends