Author: Uri Blass
Date: 09:18:17 09/27/02
Go up one level in this thread
On September 27, 2002 at 11:36:44, Gerrit Reubold wrote: >On September 27, 2002 at 11:15:27, Uri Blass wrote: > >>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 > >I disagree, why should the odds for door 1 change when door 999999 is opened? > >Gerrit What do you disagree about? Suppose we play 1000000 games when I always choose door 1 and the host always open the other doors except door 432102. Suppose that the car is in door i in game i. Do you agree that 999998 games are canceled? Do you agree that in the games that are not canceled you can win 1 of 2 if you do not switch? Do you agree that it means that the probability to win is 1/2 after you know that the game is not canceled? I did not understand the second reply of Rolf so I did not answer about it. Uri
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