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Monty Hall Problem
Simple Explanation to the Monty Hall Problem
To me the most interesting thing about this entertaining problem is not the puzzle itself but instead how complicated of most of the explanations of the answer on the internet are. My explanation is pretty simple.
The Problem
In one of the oft used scenarios on the old Lets Make a Deal Show hosted by Monty Hall, the contestant is told that a car (good prize) lies behind of one of three doors and that zero value booby prizes lie behind the other two door. If the contestant picks the right door he will get the car.
After the contestant first picks a door, Monty would open one of the other doors hiding a booby prize (since there are 2 booby prizes, there will always be one left) and offer the contestant the opportunity to change his choice of door to the remaining closed door.
The Problem: Does it benefit the contestant to choose to change his choice of doors at this point?
The Answer
At first glance it appears that it does not matter if the contestent accepts Monty's offer since he is choosing between 2 doors, one of which contains the car. However this is not the case.
In fact, the contestant should alway change his choice and choose the other door. By doing so, he has a whopping 66.6% chance of winning the car.
The Simple Explanation
Let' assume the contestant changes his choice of doors every time and see what happens.
- When he initially picks the door with the car he will lose every time by changing his door choice.
- When he initially picks the booby prize he will win every time by changing his door choice because Monty eliminates the other booby prize by first opening the remaining losing door.
- He will initially pick the booby prize 2 out of 3 times and will thus win overall 2 out of 3 time by always changing his choice of door.
That's all there is to it.
Gerry Rodman
If they touch our Social Security...