3 ms·
The notion of revealing the goat before you make your second choice is a bit of a distraction. It becomes a lot more clear if you realize that in your first ch
by hamburglar 12y ago
The notion of revealing the goat before you make your second choice is a bit of a distraction. It becomes a lot more clear if you realize that in your first choice, you're dividing the doors into two groups: the group you choose has a 1/N chance of having a car in it, and the group you didn't choose has a (N-1)/N chance of having a car in it. Now, imagine that without opening any doors, Monty said: if you're willing to switch to the N-1 group, you win if there's a car in any of them. Do you take it? Of course.
- lukasb 12y agoYeah this is it I think. If I can restate more simply for the 3-door case: You pick. The doors are now in two groups: your door (1/3 chance) and the other two doors (2/3 chance). The host picks. The second group is now reduced to a single door, still with 2/3 chance. Now you decide - stick with the door with 1/3 chance, or switch to the door with 2/3 chance?