Author: Uri Blass
Date: 08:15:27 09/27/02
Go up one level in this thread
On September 27, 2002 at 11:09:41, Gerrit Reubold wrote: >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. The car is not moving but my knowledge is changed. The fact that there is a game changes the probability. Let play 100000 games when the car is behind door i in game i. Wehn the car is behind door 1 you lose by switching. When the car is behind door 432102 you win by switching In other cases there is no game. The number of wins equal to the number of losses and it mean that the probability is 1/2. Uri
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