Presentation on theme: "Probability and Statistics"— Presentation transcript:
1 Probability and Statistics The Monty Hall ProblemProbability and StatisticsProbability Theory
2 HistorySeptember 1991, a reader of Parade asked a question to the “Ask Marilyn” columnIf 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 responseMatthew Carlton, Cecil Adams, and Keith Devlin later gave their reasoning that aligned with Marilyn’s
3 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 1970s3 doors are shown and the contestant picks oneOne door has a car, the other two have nothingA door that wasn’t picked is opened to reveal it’s emptyThe contestant has a choice to stick with their door or change to the other one
5 Explanation The choice isn’t luck but based on probability 1/3 chance of picking the car at the beginningOnce a door is eliminated, the chance of winning a car between the last 2 doors is NOT 50-50Need to look at 2 options:Always switchingAlways staying
6 Explanation Cont’d Always stay: Always switch: 2/3 chance of picking a door with nothing1/3 chance of picking the door with the carAlways switch:2/3 chance of picking a door with the car1/3 chance of picking a door with nothing
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