You are at a game show, and the host shows you 3 doors. He tells you that behind 1 of the doors, there is a BMW car. He also tells you that there is a monkey behind each of the other doors. The point of the game is to choose the door with the car. No matter what door you pick at first, the host opens another door which contains a monkey. So now you are looking at 3 doors; one which is open (showing the monkey), the closed door which you chose, and the other closed door.

The host allows you to switch doors at the last minute (from the one you chose before, to the one that you didn’t choose). You are also allowed to stick with your first choice.

The question is, should you switch doors? Or should you stick to your original choice. Why?