Problem #104 MEDIUM
The Three-Door Problem Nobody Gets Right
Paradox Probability Logic
Problem Statement
You are on a game show with 1,000 doors. Behind one is a car; behind the rest are goats. You pick door #1. The host opens 998 other doors, all revealing goats. One door remains: door #482. He offers you a switch. What is the probability of winning if you switch? Now here is the real twist: what if the host does NOT know where the car is and opens doors randomly — and just happened to reveal 998 goats by luck? Does this change the answer? Why?
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