Author: Gerrit Reubold
Date: 08:09:41 09/27/02
Go up one level in this thread
On September 27, 2002 at 11:02:59, Uri Blass wrote: >On September 27, 2002 at 10:32:18, Gerrit Reubold wrote: > >>On September 27, 2002 at 10:18:19, Uri Blass wrote: >> >>>On September 27, 2002 at 10:04:42, Gerrit Reubold wrote: >>> >>>>On September 27, 2002 at 09:45:47, Uri Blass wrote: >>>> >>>>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? >>> >>>No >>>> >>>>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? >>> >>>No >>> >>>in 100000 cases you are going to have 999998 cases when there >>>is no game >>>1 case when there is a game when it is a good idea to switch and >>>1 case when there is a game when it is a bad idea to switch >>> >> >>I discuss only the situation when there is a game. The two cases when there is a >>game are _NOT_ equally likely. >> >>When the game starts: >>The car is with 999999/1000000 probability behind one of the doors 2..1000000. >> >>Do you agree? > >Yes >> >>Now 999998 doors are opened, the 999999/1000000 probability is still correct. > >Before I see the result of opening the doors I agree. > >>The car is with 1/1000000 behind door 1 and with 999999/1000000 behind door >>432.102 >> >>Do you agree? > >No > Why not? The car is not moving. It is not more likely that it is behind door 1 than before the doors were opened. Perhaps we should play such a game against each other, the one who is right will get rich, the other will get poor :-) Greetings, Gerrit >Not seeing a car is important in the 999998 doors is an important information >that changes the probability. > >Uri
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