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  • oystein
    +4

    The point lies in what Monty does when you choose a door. He deliberately opens a door that doesn't have anything behind it. Thus making sure that the 2/3-probability still lies with the door(s) you haven't chosen. I had my students try it out on eachother and it pays off to switch in two thirds of the cases.

    • ofest
      +5

      I had no idea what the Monty Hall problem was. Upon looking it up, I think I can explain it:

      Monty introduced NEW INFORMATION into the system once he exposed the door that was a zonk (he told the contestant which door NOT to choose). The contestant had NO new information on the door he/she chose, but new (and beneficial) information on the doors he/she didn't choose. To benefit from that new info, the logical choice was to switch.

      If that still doesn't make sense, i can try to explain it differently.

    • ColonBowel
      +2

      Why isn't the choice to stay or switch independent from the first choice to choose one of the 3?

      • redalastor
        +5

        Do you agree that when you choose your initial door, the probability of being right is 1/3? Baring a switcheroo behind the door, that probability cannot change. The car won't jump to or away from the door.

        The other doors also have 1/3 chances. Until Monty opens one, now that door has 0/3 chances of being right. You door is still 1/3, we already established it can't change. There's now 1/3 unaccounted for. Where did it go? To the remaining door which brings it to 2/3.

        • ColonBowel
          +4

          Ohhhhhhhhhhhhhhhhhh! I got it now. Thanks!