I know it's been answered, but I had this answer before reading the post so I'm posting it anyways.DasDestroyer said:
At the time you picked a door, you had one chance in three to be right. But because no matter what door you choose, the guy eliminates one wrong possibility, there is a chance in two that the other door has the prize, while only a chance in three that the door you originally picked has it. Therefore the probability is higher that the prize is under the other door, and you should switch.
Explained a different way: it's only a bad idea to switch if the door you picked at the beginning was the right one. Since there is only one in three chances of that, that means two times out of three changing your pick is better.
Explained a different way: it's only a bad idea to switch if the door you picked at the beginning was the right one. Since there is only one in three chances of that, that means two times out of three changing your pick is better.
DasDestroyer said:
Does the guy in the back, the one who guessed what colour his hat was (easily, since he could see the other three) tell everyone else? I'm assuming no, but if yes, the answer is that the third person would get the right answer.
However, if he does NOT, then the second person gets the colour right. The second person thinks "if both my hat and the hat of the guy right in front of me were the same colour, the third guy would have known what colour his hat was. Since he doesn't, my hat isn't the same colour as the guy in front of me", and therefore guesses his hat colour.
However, if he does NOT, then the second person gets the colour right. The second person thinks "if both my hat and the hat of the guy right in front of me were the same colour, the third guy would have known what colour his hat was. Since he doesn't, my hat isn't the same colour as the guy in front of me", and therefore guesses his hat colour.