Communicator (communicator) wrote,
Communicator
communicator

The Monty Hall paradox

Here is a maths problem, which might amuse you. Answer below the cut, plus links to a proof and a demonstration.

But first the set-up. Monty Hall ran a quiz show in the US. The contestant was confronted with three doors. Behind one door was an expensive car, behind the other two a relatively worthless prize such as a goat. The contestant had to pick one of the doors. Before he could open it Monty Hall opened one of the other doors, showing a goat behind it. The contestant had to decide whether to stick with his original choice or switch to the other unopened door.

Stick or switch? I think the superficial intuitive answer is that it makes no difference. There are two doors. One has a car, one has a goat. There is an equal chance that the car is behind either door. Right?



No - in fact switching to the other door doubles your chances of getting the car. Whichever door you started with, you double your chances by switching to the other one.

Don't believe me? I didn't believe it myself. But here is an explanation. Here is an online demonstration showing that it's true. Here is a discussion on crooked timber which might help to elucidate.



EDIT - this must be doing the rounds today, there's a long disucssion here http://www.metafilter.com/mefi/34449#704578

For me the key point is that Monty adds information because of the rule that he never opens the 'right' door, although the information is hidden because that rule is never made explicit.
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