The role of probability in solving the Monty Hall problem

[Jenny A]

One more simple way to look at it. When you choose one door the probability of the door you choose having the car is one third. There is a two thirds chance that the car is behind one of the other two doors. By showing you which of the other two doors not to choose, Monty is letting you take all of the two thirds probability in a single door. So you can either keep your one third or opt for two thirds. It is exactly the same as if you chose one door and then Monty said you could either keep your door or take the other two doors.