The Monty Hall Problem
The following problem is taken from a quiz show on TV that really
existed (or still exists). It is an interesting topic to discuss in
almost any group of people because even the most intelligent often
get into trouble, and is (in other languages) referred to as the Goat Problem.
New: In compliance with the current
domain grabbing hysteria, this page is now also available as
http://www.ziegenproblem.de/,
which is easier to memorize - at least for speakers of German.
The Scenario
The quiz show candidate has mastered all the questions. Now it's
all or nothing for one last time: He is lead to a room with three
doors. Behind one of them there's an expensive sports car; behind
the other two there's a goat. (Don't ask me why it's a goat. That's
just the way it is.)
The candidate chooses one of the doors. But it is not opened; the
host (who knows the location of the sports car) opens one of the
other doors instead and shows a goat. The rules of the
game, which are known to all participants, require the host to
do this irrespective of the candidate's initial choice.
The candidate is now asked if he wants to stick with the door he
chose originally or if he prefers to switch to the other
remaining closed door. His goal is the sports car, of course!
The Question
The question now is:
- Is the candidate better off if he sticks with his original choice,
- are his chances better if he switches, or
- does it not matter whether he switches or not?
Enjoy the riddle.
Here's the solution.
Frederik Ramm, 2004-11-18