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Forum URL: http://www.cut-the-knot.org/cgi-bin/dcforum/forumctk.cgi
Forum Name: Middle school
Topic ID: 64
Message ID: 7
#7, RE: Monty Hall Problem
Posted by Alan Cooper on May-10-02 at 07:17 AM
In response to message #6
I don't know about the others, but anyone who believes your argument should easily be convinced that although the earth may not definitely be flat it at least has a 50% chance of being flat.Pick a planet at random. Either it is flat or it is not flat. Two possible outcomes. So the probability of being flat must be 50%

This illustrates a common fallacy in analysis of probabilities.
The fact that an experiment can be described as having two possible outcomes does not mean that both are equally likely.

To convince you that the conclusion of equal probabilities is wrong in the Monty Hall problem, consider the situation with a million doors - one car, the rest goats. Monty says Pick one and promises to show you 999998 goats. You have a 1 in a million chance of picking the car to start with. If you didnt choose the car to start with switching will give it to you for sure. If you don't agree that switching is the better strategy I'd like to meet you in Las Vegas.