Author: Gerrit Reubold
Date: 05:50:27 09/27/02
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On September 27, 2002 at 08:22:06, Sune Fischer wrote: >On September 27, 2002 at 08:14:28, Gerrit Reubold wrote: > >>Hi Sune, >> >>On September 26, 2002 at 14:47:32, Sune Fischer wrote: >> >>I disagree, I am sure it doesn't matter whether the host opens a door (with a >>goat) KNOWING where the car is or by SHEAR LUCK. The candidate should switch in >>either case, thus improving his winning odds from 1/3 to 2/3. Of course, if the >>host doesn't know and opens the door with the car (accidently), the game is over >>:-) > >Ok, well at least we agree that if he KNOWS he should switch. > >So suppose the host doesn't know, and the host opens a door to a goat. > >What does this tell us? >Well, since he didn't know, it means he either had a 50% probability of opening >to a goat, or a 100% probability. > >He gets 100% probability if we are sitting on the car, and he gets 50% if the >car is behind the one of the doors he had to choose from. > >The odds of picking a goat if you have 100% probability is higher than if you >only have 50% (obviously), okay? I don't care what that probability was _before_ he opened the door. The door with the goat is _now_ open. > >Thus we now know it is more probable that we did pick the door with the car, >because the host was so lucky to pick one with a goat, which is a lot more >proabable if he had nothing but goats to choose from. > >-S. The candidate can't read the host's mind, he can't know whether he was lucky or did know the door with the car. The candidate shouldn't care, he should just switch. Obvious to me, as obvious as the opposite is to you. Greetings, Gerrit
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