Concise, intuitive explanation of the three-door problem

Roderick 2022-04-20 09:01:26

Although I haven't seen the movie, I am very interested in the three questions, and I have browsed many comments and answers. Now I will describe my own concise and intuitive explanation as follows. It seems that it does not require much brains. It took a lot of brains.

If only one gate can be chosen at the beginning, the probability is 1/3. There is no doubt
that if you are asked to choose two doors at the beginning, the probability is 2/3. There should also be no controversy.
The rules of the game are to let you choose 2 doors by changing.
As for which of these two doors does not have a car, the host has already ruled out one for you, so you don't have to worry about it anymore.
As for whether the host can rule out the right or not, it is the core of everyone's controversy. If the host knows in advance that one row is accurate, your chance of winning the lottery will be locked in 2/3, but if the host does not know, it is also a random row, then you The probability of winning the lottery is reduced from 2/3 to (2/3*1/2=1/3), which is the same as the probability of choosing a car before, that is, you can change it or not.

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Extended Reading

21 quotes

  • [Micky gives Jill her fake ID for the Vegas casinos]

    Jill Taylor: Uh, I don't like my name.

    Micky Rosa: Why not?

    Jill Taylor: 'Sierra Sommers.' Do I look like a Sierra?

    Micky Rosa: Well, you have a lot of clever outfits. You'll figure it out.

    Kianna: Just pretend you don't speak English. Then you don't have to change your hair.

  • [Micky talks to the team one last time before they play the Vegas casinos]

    Micky Rosa: At all times, you don't know each other. Let me say that again, you do not... know each other... ever. Oh, and what's our motto?

    Jill Taylor: Don't get caught counting.

    Fisher: Don't get caught counting.

    Kianna: Don't get caught counting.

    Micky Rosa: Thank you very much.