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View Diary: Morning feature: The Monty Hall problem (with poll and statistics questions answered) (310 comments)

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  •  It's simple really. (5+ / 0-)

    When you make your first door pick, you divide the doors into two groups: "your door" and "Monty's doors".

    Behind Monty's doors are either a goat and a car, or two goats. In the full knowledge of what is behind those two doors, Monty eliminated one goat.

    That's exactly what you would do, so suppose you were given the equivalent choice, instead of Monty doing it for you. You can either pick your one door, or you can open both of Monty's doors and then eliminate one of them, in the full knowledge of what's behind them.

    Obviously you will eliminate a goat, just as Monty did. You're not going to eliminate the car if it's behind one of Monty's doors.

    So even though this is an exactly equivalent situation (i.e. you will make the same elimination Monty did) the choice is clearer: you are being asked to choose between one door ("your door") or two doors ("Monty's doors"). Your odds are twice as good with two doors as with one. See?

    One nation, indivisible.

    by Doctor Frog on Tue May 05, 2009 at 07:09:27 AM PDT

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