Author: Gerrit Reubold
Date: 07:04:42 09/27/02
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On September 27, 2002 at 09:45:47, Uri Blass wrote: >On September 27, 2002 at 08:50:27, Gerrit Reubold wrote: >> >>I don't care what that probability was _before_ he opened the door. The door >>with the goat is _now_ open. > >Suppose for the discussion that the candidate also guess door 1 >and the host always open door 3 in case that door 1 has a goat. Do you mean "... in case that door 3 has a goat" ? (I assume that the host _must_ open a door, he is not allowed to keep both doors closed.) I discuss this situation: - The candidate chooses door 1 - The host chooses (say) door 3, and is lucky, there is a goat in door 3 So there _is_ a game! Now the candidate should switch and double its winning chances. Do you agree? If you don't agree: Consider the game with 1.000.000 doors, the candidate chooses door 1. The host opens 999.998 doors, without knowing where the car is. By incredible luck all those doors have goats behind them. There is now door 1 and door 432.102 closed. So again there is a game! Do you agree that the candidate should switch? BTW, this seems all obvious to me, maybe we are discussing different situations? Greetings, Gerrit > >If I understand correctly you say that the candidate should switch >and get probability of 2/3. > >Do you agree? > >Let assume case i means that the car is behind door i. > >In case 1 the car is behind door 1 so the candidate win only if he does not >switch. >In case 2 the car is behind door 2 so the candidate win only if >he switchs. > >In case 3 the car is behind door 3 so the host expose the car so there >is no game. > >Do you agree? > >The probability for every case is 1/3 before the game start. > >Do you agree? > > >If we know that case 3 does not happen and this is what we know >after the host opened door 3 and found no car then it means >that there are only 2 cases and the probability for every case is >(1/3)/(2/3)=1/2. > >Do you agree? > >It mean that switching is going to give you probability 1/2 > >Do you agree? > >I did not spend some minutes to try to understand >sune's post but I believe that he also understood the point. > >Uri
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