The Monty Hall Problem: Why Switching Wins 2/3 of the Time

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The Monty Hall Problem: Why Switching Wins 2/3 of the Time

DEV Community: tutorial·White Oak Intelligence·1 day ago

#hesXKr8P

#dev #door #host #probability #switch #pick

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In This Article The Question The Intuition Trap: Why 50/50 Feels Obvious The Exhaustive Case Proof The Bayesian Derivation The Generalized N-Door Problem Python Simulation: 1,000,000 Trials Business Application: Bayesian Updating Under New Evidence The Question You are a contestant on a game show. In front of you stand three closed doors. Behind one of them is a car; behind the other two are goats. You select a door — say, Door 1. The host, who knows exactly what is behind every door, opens a different door — say, Door 3 — to reveal a goat. The host always reveals a goat and always offers you the chance to switch. He now asks: do you want to switch to Door 2, or stay with Door 1? The question, stated precisely: given everything you now know, what is the probability that the car is behind Door 2? And what is the optimal strategy — switch or stay? The answer is that you should always switch. Switching wins with probability 2/3; staying wins with probability 1/3.…

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The Monty Hall Problem: Why Switching Wins 2/3 of the Time