The Monty Hall Problem

You are on a game show. Three doors. One car, two goats. You pick door 1. The host opens door 3 to reveal a goat. Do you switch?

The Answer

Switch. Your odds go from 1/3 to 2/3.

Why

When you picked, there was a 1/3 chance you were right and 2/3 chance the car was behind one of the other two doors. The host always reveals a goat, so the 2/3 probability concentrates on the remaining unopened door.

Most people find this deeply unintuitive. That is what makes it interesting.