The Monty Hall Problem

Level 2●●●○○ Medium~5 min

Problem

Three doors hide one car and two goats. You pick door 1. The host — who knows what is behind each door and always opens a goat door you did *not* pick — opens door 3, revealing a goat. He offers you the chance to switch to door 2. Should you switch? Quantify the win probabilities. Why does the answer depend on the host's protocol?