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No, it's correct. The easiest explanation, IMHO, is: 1. If you already selected the correct door, you should not switch, obviously. Equally obviously, the od
by newacct583 5y ago
No, it's correct. The easiest explanation, IMHO, is:
1. If you already selected the correct door, you should not switch, obviously. Equally obviously, the odds of being in this state are 1/3, because your initial choice was random.
2. If you did not select the right door, then the host clearly revealed the only one of the two remaining doors without a prize. In this state, you clearly should switch to the only door remaining, which contains the prize.
That is, the likelihood that switching will get you the prize is 2/3, because it corresponds to the states where you initially guessed wrong.
- dionidium 5y agoThis is a very good explanation. I hope you won't mind if I say the exact same thing you did in just a slightly different way that might help it click for someone still not getting it. Your initial chances of choosing correctly are 1 in 3. So the car is behind the door you chose 1/3 of the time. After the host reveals which of the 3 doors definitely does not have the car it's still the case that your initial choice will have the car 1/3 of the time [0]. That means the other door must contain the car 2/3 of the time. So you should switch. [0] The haters are correct that the host hasn't changed the odds that your initial choice is correct. They just aren't tracking the implications of that fact.