Author: Roy Eassa
Date: 14:33:00 09/25/02
Go up one level in this thread
On September 25, 2002 at 16:31:55, Joachim Rang wrote: >On September 25, 2002 at 15:46:14, Rolf Tueschen wrote: > >>On September 25, 2002 at 14:35:29, Joachim Rang wrote: >> >>>On September 25, 2002 at 12:38:06, Rolf Tueschen wrote: >>> >>>>Please take a look at my revolutionary solution of this confusing problem: >>>> >>>>http://hometown.aol.de/rolftueschen/monty.html >>>> >>>> >>>>At first I went into the net and collected all sort of data for my page. I >>>>wanted to show how important methods and methodology are for science and also >>>>statistics. In special the exact defining of the terms. >>>> >>>>Then suddenly I had the inspiration and in a few minutes whitewashed a million >>>>people who as pupils, students or even professors let them be proved wrong by >>>>Marilyn vos Savant who has an IQ of 228. For decades now the Monty Hall Problem >>>>is taken as example for conditioned probability, which is wrong! >>>> >>>>Hope you enjoy my revelations. Please tell me if you want to comment. >>>> >>>>Rolf Tueschen >>> >>>hm, I didn't read all your stuff (its simple too much), but if I understand you >>>correctly, you claim, that the probability is 50% in both cases (switch or >>>stick). Right? >>> >>>Than you're wrong ;-) >>> >>>Only a simple note: >>> >>>you wrote: the help of the host....(There is no help - Rolf Tueschen) >>> >>>actually there is help. Because the host can not choose to open a door _before_ >>>you made your choice. He has to wait, which door you choose and than to open >>>from the left two doors the wrong one. This condition you may interpret as help >>>from the host. >> >>I like your reasoning. But it can't succeed. I am sure you saw that I already >>accepted that - sure - the host "helped" to bring the situation from 1/3 to 1/2. >>But unfortunately he didn't help more. But I'm open for explanations. Let me ask >>the following: Are you aware of the difference between a unique situation and >>the general question about the general probability in the long run? Because I do >>not deny that say a group of hundred people as a group have more wins if they >>switch! But the problem we have here, how you want to prove the increase above >>1/2 for a single unique case. I think that this is the crucial point of the >>whole problem. And I'm sure that all the experts who opposed Marilyn vos Savant >>at the beginning did it because they knew that for the particular case >>conditioned probability could not help. But then they were influenced by the >>rich vocabulary of the smart woman. >> >>Rolf Tueschen > > >Okay, let's try: > >Assumptions: > >1. There are 3 doors, each with a winning probability of 1/3 >2. The host has to open a "wrong" door. > >Setting 1: > >The host anounces which door he will open _before_ you make your first choice. >Because he has to open a "wrong" door, after that the chances of the two >remaining doors are 1/2 > >Setting 2: > >The host has to open a door _after_ your first choice. If you choose a "wrong" >door the host is _forced_ to open the only remaining "wrong" door. This changes >the setting similiar to one, when you have to choose between three doors with a >probability of 2/3. > >Okay I can't explain it scientifically correct, but the "mystic" lays in the >dependency of your first choice and the second of the host. OK, I'll take my shot at wording the explanation: "If n is the starting number of doors... The door you choose always has (from your perspective) a 1/n chance of being the winner. All the unopened doors COMBINED (assuming there's at least one) always have a (n-1)/n chance. If Monty opens one of those doors that he KNOWS is not a winner, that does not change the fact that all the (remaining) unopened doors combined have a (n-1)/n chance. But since there are now fewer of them among which to divide it, each INDIVIDUAL unopened door's chance is (from your perspective) higher than before. Thus in the 3-door example, your door has a 1/3 chance and the one remaining unopened door has a 2/3 chance of being the winner."
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