The Monty Hall Problem is a famous probability problem named for the original host of “Let’s Make A Deal.” The controversy began in 1990 when Marilyn vos Savant posed the question in her column.
The Monty Hall Problem: A contestant on a game show is asked to choose between three doors, behind one of which is a brand new car. Then the host, who knows where the car is hidden, opens one of the other doors where there is no car. The host then asks the contestant if they would like to stay with their original door or switch to the other unopened door. Should the contestant stay or switch?
Marilyn vos Savant said that the contestant should always switch doors to increase their odds of winning. This counterintuitive solution created a massive debate. Vos Savant received about 10,000 letters from readers, including many Ph.D.s, telling her she was mistaken. Many argued that after the host opens one of the doors each remaining door has a 1/2 chance of hiding the car, in which case it should not matter if you switch or stay. But vos Savant was right. When the host opens one of the doors he provides additional information. The door that he opens changes based on where the car is and which door the contestant chooses. Contestants who switch doors increase their chances of winning from 1/3 to 2/3. See the step-by-step explanation in the video.
Produced by Sara Silverstein and Matt Johnston.
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