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**Probability and Statistics**

The Monty Hall Problem Probability and Statistics Probability Theory

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History September 1991, a reader of Parade asked a question to the “Ask Marilyn” column If you’re on a game show and you can choose one of three doors where there’s a car behind one and a goat behind the other two, after picking a door, would you switch doors after being revealed one with a goat? Is there an advantage? Marilyn Vos Savant responded saying it would be better to switch, and there was a lot of controversy with this response Matthew Carlton, Cecil Adams, and Keith Devlin later gave their reasoning that aligned with Marilyn’s

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**History cont’d This dilemma was named after Monty Hall**

Monty Hall was the host of Let’s Make a Deal in the 1960s and 1970s 3 doors are shown and the contestant picks one One door has a car, the other two have nothing A door that wasn’t picked is opened to reveal it’s empty The contestant has a choice to stick with their door or change to the other one

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The big question…. Should you switch???

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**Explanation The choice isn’t luck but based on probability**

1/3 chance of picking the car at the beginning Once a door is eliminated, the chance of winning a car between the last 2 doors is NOT 50-50 Need to look at 2 options: Always switching Always staying

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**Explanation Cont’d Always stay: Always switch:**

2/3 chance of picking a door with nothing 1/3 chance of picking the door with the car Always switch: 2/3 chance of picking a door with the car 1/3 chance of picking a door with nothing

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**There is a 2/3 chance of getting the car if you switch.**

This means you have a better chance at winning if you switch!

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References https://www.khanacademy.org/math/trigonometry/prob_c omb/dependent_events_precalc/v/monty-hall-problem s

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