4 ms·
At first I agreed with you, but then I thought about the variation with 100 doors (this is what originally helped me grasp the correct answer): you choose a doo
by tomerv 5y ago
At first I agreed with you, but then I thought about the variation with 100 doors (this is what originally helped me grasp the correct answer): you choose a door out of 100 (with very slim chance of choosing the correct one), the host opens 98 of the remaining 99 doors and there are goats behind all of them. Now it's obvious that the car is in the remaining door.
If the host is opening random doors, then:
* If you chose a door with a goat, in 98/99 cases we would start the game over because the host opened the door with the car.
* If you chose the door with the car, the game cannot start over because the host can only open doors with goats.
This means that when you choose a goat, the randomness gives you another chance to choose the correct door.
- denton-scratch 5y ago"Now it's obvious that the car is in the remaining door." No. It could be behind the one you chose, surely. I understand the explanations, or at least some of them; but I still don't get it. I thought I was intelligent and numerate, and this is making me sad. I don't see why, after Monty reveals a goat and invites you to switch, you can't re-assess the probabilities from scratch. There are two closed doors, car behind one, goat behind the other, and you have no evidence which is which; therefore 50:50.
- bordercases 5y agoBut you are presented with a new option with 50:50 odds and should take it. Since the original odds were worse.