Author: Sune Fischer
Date: 05:22:06 09/27/02
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On September 27, 2002 at 08:14:28, Gerrit Reubold wrote: >Hi Sune, > >On September 26, 2002 at 14:47:32, Sune Fischer wrote: > >>On September 25, 2002 at 15:06:58, John Merlino wrote: >>>correct if you switch. The "host" has nothing to do with it, because he/she MUST >>>choose a door to open. > > >>Not entirely correct, the host has got something to do with it. The host must >>KNOW which door hides the car. It is vital that he doesn't open a door to a goat >>by shear luck, because in that case you do not get that 2/3 odds. >> > >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? 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. >Greetings, >Gerrit
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