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The Infamous Monty Hall Problem

You are presented with 3 doors (A, B, C) only one of which has something valuable to you behind it (the others are bogus) you do not know what is behind any of the doors

You choose a door

Monty then counters by

  • showing you what is behind one of the other doors (which is a bogus prize), and
  • asks you if you would like to stick with the door you have, or
  • switch to the other unknown door

The question is

should you switch?

Another question is

Does it matter?

You should always switch. At this point in the game it is not a 50/50 chance between the two doors.

I found a website that describes it like this:

This is not an example of simple probability (suppose there are two doors, therefore there is a 1 in 2 chance of the car being behind either of the doors). This is an example of conditional probability: what is the chance of something happening, given that something else already has. The something else is that Monty will never open the door to the prize.

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Page last modified on May 04, 2006, at 05:10 AM