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Old 06-15-2008, 01:40 AM
Paul Paul is offline
Join Date: Feb 2007
Posts: 7
Default One way to understand the solution to the Monty Hall problem.

For anyone else, like me, who finds it hard to understand why the non-intuitive solution to the Monty Hall problem (that one should choose to switch doors with a 2/3 chance of getting the prize) is correct, it might help to think of it this way.

Suppose you choose door one. Then Monty Hall eliminates as an option one of the other doors, and gives you the choice of switching to the remaining door, or staying put. You take that option and switch to the other unopened door. This is equivalent to Monty saying, "you can stick with door one (1/3 chance of winning the prize), or I can open both doors two and three (2/3 chance of winning the prize)."

The Wikipedia article [ http://en.wikipedia.org/wiki/Monty_Hall_problem ] has a helpful probability-tree diagram and proof using Bayes's theorem. The roulette wheel diagrams on this page are also helpful: [ http://math.ucsd.edu/~crypto/Monty/montybg.html ].

(On a side note, it must have been very odd -- or flattering -- or something -- for the real Monty Hall to have found himself the demon or genie in a quasi-philosophical paradox.)
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