1. You should switch. If contestants switch every time, one of
two things happens:
(a) With probability 2/3, the contestant picks a wrong door.
Monty Hall shows the prize behind the other wrong door, and the
contestant switches to the door hiding the car.
(b) With probability 1/3, the contestant picks the right
door, Monty Hall reveals either the donkey or the bananas, and
the contestant switches to the other "zonk" prize.
So, with probability 2/3, the "switch" strategy will elicit the car.
This is one of the most famous (and widely-debated) probability problems of
the past ten years. For more information, and a simulation to show that
the above solution is truly correct, check out the following website:
http://www.cut-the-knot.org/hall.shtml