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Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?
Do any of you have any noteworthy experiences where knowledge of math helped you in an unusual way?
https://en.wikipedia.org/wiki/Monty_Hall_problem
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Get Those Brain Cells Working: The Monty Hall Problem
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squatcho, n.:
The button at the top of a baseball cap.
-- "Sniglets", Rich Hall & Friends
(Score: 2, Insightful) by Anonymous Coward on Friday July 29 2016, @02:31PM
Let's try a different explanation, then.
You pick a door.
One third of the time, you have picked the one with the car.
Two thirds of the time, you have picked one with a goat.
Then the rules force Monty to act based on your choice.
In the 1/3 case, Monty can choose either of the other doors (they both have goats), but it does not matter what he chooses. The remaining door will have a goat.
In the 2/3 case, Monty has no choice - he *must* eliminate the only other door with a goat. The remaining door must have the car.
In the 1/3 case, if you switch, you get a goat
In the 2/3 case, if you switch, you get a car
The reason that it is not 50-50 is Monty lack of choice. No matter what he does, he cannot change the situation you find yourself in when the "do you switch"? question is asked. You controlled that with your first choice ... and there were three options at the beginning.