The Monte Hall Problem: This is a famous (or infamous!) probability paradox. In
ID: 3070055 • Letter: T
Question
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? 2.15Explanation / Answer
Answer:
After Monte Hall opens the door with the booby prize while for the initial pick, the player knows that the special prize presented ithin among 2 doors . The contenstent had to pick one out of the 3 doors.
Three possibilities of arrangements are
Car Goat Goat
Goat car car
Goat Car Goat
here winning probability is only 1/3.
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.
Staying at Door 1 Staying at door 2
Wins Car Wins GOat
wins Goat Wins car
Wins Goat WIns car
So by switching there is a difference