The Monte Hall Problem: This is a famous (or infamous!) probability paradox. In

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? 2.15

Explanation / 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

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