@ethanparkerlife: Everyone answers yes. The math answers no. Here is the machine behind it. Take one million people. All of them take the test. Only one actually has the disease. The test is 97% accurate so it almost certainly catches that one person. One real positive. Now the other 999,999 people. They are healthy. But 97% accuracy means a 3% error rate. Three percent of 999,999 is about 30,000 people. Healthy people. Positive tests. So the pile of positive results holds about 30,001 names. One sick. Thirty thousand healthy. Your chance of actually being sick after a positive test is 1 in 30,001. That is 0.003%. Not 97%. 0.003%. The accuracy of the test and the chance you are sick are two different numbers. Most people swap them without noticing. The first number measures the test. The second one measures you. Why does your gut get this so wrong? Because your gut only sees two numbers. Rare disease. Accurate test. It never multiplies them against a million healthy people. The base rate is invisible so the brain just deletes it. That deletion is the entire error. This machine runs everywhere. Airport security. Drug tests at work. Fraud alerts from your bank. Spam filters. Any system hunting for something rare will bury the one real case under a mountain of false alarms. The rarer the thing you hunt, the taller the mountain. That is why a single positive on a rare condition means one thing. Retest. A second independent positive changes the math completely. You can check every number here yourself. One million times 3% is 30,000. That is the whole trick. No statistics degree required. Just one multiplication most people never do. ... The test was never wrong about being 97% accurate. You were wrong about what that number measures. It measures the machine. It never measured you.
