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The Three Doors

There are countless variations of this problem, with lions and virgins hidden behind doors, and poor prisoners that have to chose a door and get eaten or survive. This version here is less violent and has an interesting twist:

The quiz master explains: You are allowed to open one of three doors, if you open the correct one you will find a chest with hundreds of diamonds. Open one of the other two doors and you will get nothing!

Mike looks at the three doors, but they all look the same, there is no hint as to which one is the correct one. Finally he says: "I choose this door" and points to one of them.

The quiz master looks at him and replies: "today I am in a good mood, and therefore I will now give you a hint: I will open one of the two doors you did not chose, and will show you that this is one of the wrong doors". He goes over and opens one of the remaining doors and everyone can see that there is nothing behind it.

He continues "Now I give you a second chance: you can either go with the door you originally chose, or switch to the other door that is still closed".

And the question to you: should Mike go with the door he originally chose, or should he switch? What is the probability that he wins?

Hint: If Mike plays the game correctly he can boost the probability of a win to well over 50%!

This problem is known as the Monty Hall Problem and many web pages discuss it.

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