The Monty Hall Problem

You’re on a game show: three doors – one car, two goats. You pick door 1. The host (who knows where the car is) opens door 3, revealing a goat. He offers to let you switch to door 2. Should you? Yes – switching wins with probability 2/3, staying wins 1/3. This counterintuitive result, popularised by Marilyn vos Savant in 1990, generated thousands of angry letters (including from PhD mathematicians). The key: the host’s choice gives you extra information. The conditional probability changes.