#base-rate

1 articles

01 ·Probability & Statistics·FREE·PAPER·16 min read Bayes' Theorem from Scratch — Why a 99% Accurate Test Can Be a Coin Flip Bayes' theorem is four symbols that reverse a conditional probability, and the single most common way people get probability wrong. This article derives it line by line from the definition of conditional probability, names its four parts, then works a medical test all the way to the number: a test with 99% sensitivity and 99% specificity, applied to a disease 1% of people have, turns a positive result into a 50% chance of being ill. Ends on the base-rate fallacy, sequential updating, and where the prior comes from.