2.15 The Monte Hall Problem: This is a famous (or infamous!) probability paradox
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Question
2.15 The Monte Hall Problem: This is a famous (or infamous!) probability paradox. In the television game show Let's Make a Deal, host Monte Hall was famous for offering contestants a deal and then trying to get them to change their minds. Consider the following: There are three doors. Behind one is a special prize (e.g., an expensive car), and behind the other two are booby prizes (on the show, often goats). The contestant picks a door, and then Monte Hall opens another door and shows that behind that door is a booby prize. Monte Hall then offers to allow the contestant to switch and pick the other (unopened) door. Should the contestant switch? Does it make a difference?Explanation / Answer
I think that the contestant should switch to the other door as the contestant who switch have a (2/3) chance of winning the car while contestants who stick to their initial choice have only a (1/3) chance under the given conditions.
For the given conditions the player knows that the special prize is present within among the 2 doors after Monte Hall opens the door with the booby prize while for the initial pick, the contestant had to pick one out of the 3 doors.
Now,the three possible arrangements of one car and two goats behind three doors and the result of staying or switching after initially picking door 1 in each case:
Thus it can be seen from the table that a contestant who stays with the initial choice wins in only one out of three of these equally likely possibilities while a contestant who switches wins two out of three times.
Thus switching makes a difference.
Behind door 1 Behind door 2 Behind door 3 Result if staying at door 1 Result if switching to the door offered Car Goat Goat Wins Car Wins Goat Goat Car Goat Wins Goat Wins Car Goat Goat Car Wins Goat Wins CarRelated Questions
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