Monty Hall Problem
In a game show, the host tells you there are three doors in front of you. Behind one of them is a chest full of gold, and behind the other two are empty. The host asks you to choose a door and you picked one. Then the host opens one of the unpicked door and behind it is empty. Now he asks you whether you would like to change your choice? Would you, my friend?
The answer to this problem is as follows. Suppose you do not change, the chance of you picked the right door is 1/3 in the beginning. After the host shows the empty door to you, the chance of you picked the right door is 1/2, even you didn’t do anything. Suppose you do change your choice, there are two cases. In the first case you picked the gold chest first, then you change, you are sure to lose. The probability of this happens is 1/3. In the second case you picked the empty door first, then you change, but now you are sure to win since there is only one door left which is the chest of gold. The probability of this happens is 2/3 since in the begin there are two empty doors out of three doors. So the probability of you win is 2/3 should you change your choice and 1/2 if you do not change.
This problem is first appear in a game show and therefore is named after the host “Monty Hall”.
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