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Re: Toughest Game Show Question

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Am 11.01.2012 02:44, schrieb Kaz Kylheku:
> On 2012-01-10, Bill Reid <hormelfree@gmail.com> wrote:
>> On Jan 9, 8:56 pm, divya bisht <bisht88.di...@gmail.com> wrote:
>>>
>>> You are on a game show and there are three doors. The presenter tells
>>> you that behind one of doors there is a car and behind the other two
>>> are goats, if you pick the car you win it. After you have picked a
>>> door the presenter opens a different door with a goat behind it, he
>>> then gives you the chance to change what door you open, what should
>>> you do?
>>>
>> OH NO, THE DREADED "MONTY HALL" PROBLEM, IT'S BEEN AT LEAST A
>> DECADE SINCE I'VE SEEN THIS MONSTROUSITY REAR IT'S UGLY HEAD IN
>> USENET!!!!!!!
>>
>> The answer is that it doesn't matter, your odds are still one
>> in three no matter what you do...but wait, does it matter if the
>> presenter knows what's behind the doors and shows you the goat
>> to make the game more interesting?  Let's see what happens with
>> the "regs" here, might be fun...
> 
> I think you an easily solve this by a simple division into cases,
> and simple probabilities.
> 
> Look Ma, no conditional probability, no Bayes' theorem.
> 
> 
> Suppose Monty always reveals the goat. (This builds suspense in the
> audience and is good for the show's ratings, which are more important
> than whether or not cars are given away.)
> 
> 
> There are two cases:
> 
> Case 1: (p = 2/3) You picked the goat.
> 
> Monty knows that this case is occurring, and reveals to you the other goat! So
> you must switch to get the car, and by switching the car is guaranteed.
> 
> Case 2: (p = 1/3) You picked the car.
> 
> In this case, you must not switch; you're already on the car.
> Of course Monty reveals a goat in this case also.
> 
> 
> Now you don't know which of these cases you are in. But you do know
> that one of these cases requires switching and the other requires
> staying and that the one that requires switching occurs with p = 2/3, and the
> one that requires staying occurs with p = 1/3.
> 
> This essentially translates to "the probability that you must switch in order
> to win the car is 2/3", and that translates to "the probability that
> the car is behind the door you did not pick in round 1 is 2/3".
> 
> If you do not switch, you are betting on being in Case 2, which is p = 1/3: the
> same odds as a one-round draw.
> 
> If you switch, you are betting that you are in Case 1, where you have p = 2/3
> odds, an improvement.
> 
> 
> 
> Switching: no brainer.

My simulation shows that by switching your total chance to win
the car is 1/2 or probability 0.5

I think this is true, due to the fact that by switching you might
go off the car choice.

/Str

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Re: Toughest Game Show Question Bill Reid <hormelfree@gmail.com> - 2012-01-10 06:47 -0800
  Re: Toughest Game Show Question tom st denis <tom@iahu.ca> - 2012-01-10 07:11 -0800
    Re: Toughest Game Show Question falk@rahul.net (Edward A. Falk) - 2012-01-11 00:05 +0000
  Re: Toughest Game Show Question Eric Sosman <esosman@ieee-dot-org.invalid> - 2012-01-10 11:23 -0500
  Re: Toughest Game Show Question John Gordon <gordon@panix.com> - 2012-01-10 16:48 +0000
    Re: Toughest Game Show Question Seebs <usenet-nospam@seebs.net> - 2012-01-10 19:15 +0000
      Re: Toughest Game Show Question Keith Thompson <kst-u@mib.org> - 2012-01-10 13:27 -0800
        Re: Toughest Game Show Question James Kuyper <jameskuyper@verizon.net> - 2012-01-10 16:57 -0500
        Re: Toughest Game Show Question Seebs <usenet-nospam@seebs.net> - 2012-01-10 22:39 +0000
  Re: Toughest Game Show Question Stephen Sprunk <stephen@sprunk.org> - 2012-01-10 11:21 -0600
    Re: Toughest Game Show Question Bill Reid <hormelfree@gmail.com> - 2012-01-10 15:43 -0800
      Re: Toughest Game Show Question Stephen Sprunk <stephen@sprunk.org> - 2012-01-10 22:53 -0600
        Re: Toughest Game Show Question Seebs <usenet-nospam@seebs.net> - 2012-01-11 05:00 +0000
          Re: Toughest Game Show Question Kaz Kylheku <kaz@kylheku.com> - 2012-01-11 06:32 +0000
          Re: Toughest Game Show Question James Kuyper <jameskuyper@verizon.net> - 2012-01-11 07:22 -0500
      Re: Toughest Game Show Question falk@rahul.net (Edward A. Falk) - 2012-01-12 22:51 +0000
        Re: Toughest Game Show Question Ian Collins <ian-news@hotmail.com> - 2012-01-13 12:14 +1300
        Re: Toughest Game Show Question ImpalerCore <jadill33@gmail.com> - 2012-01-12 15:17 -0800
  Re: Toughest Game Show Question Shao Miller <sha0.miller@gmail.com> - 2012-01-10 14:33 -0500
  Re: Toughest Game Show Question Kaz Kylheku <kaz@kylheku.com> - 2012-01-11 01:44 +0000
    Re: Toughest Game Show Question Dann Corbit <dcorbit@connx.com> - 2012-01-10 23:48 -0800
      Re: Toughest Game Show Question James Kuyper <jameskuyper@verizon.net> - 2012-01-11 07:23 -0500
    Re: Toughest Game Show Question "M. Strobel" <sorry_no_mail_here@nowhere.dee> - 2012-01-11 14:33 +0100
      Re: Toughest Game Show Question Willem <willem@toad.stack.nl> - 2012-01-11 13:48 +0000
        Re: Toughest Game Show Question "M. Strobel" <sorry_no_mail_here@nowhere.dee> - 2012-01-11 18:44 +0100
          Re: Toughest Game Show Question Willem <willem@toad.stack.nl> - 2012-01-11 18:10 +0000
            Re: Toughest Game Show Question "M. Strobel" <sorry_no_mail_here@nowhere.dee> - 2012-01-11 19:23 +0100
          Re: Toughest Game Show Question James Kuyper <jameskuyper@verizon.net> - 2012-01-12 18:23 -0500
            Re: Toughest Game Show Question "M. Strobel" <sorry_no_mail_here@nowhere.dee> - 2012-01-15 19:03 +0100
            Re: Toughest Game Show Question Willem <willem@toad.stack.nl> - 2012-01-15 19:42 +0000
              Re: Toughest Game Show Question James Kuyper <jameskuyper@verizon.net> - 2012-01-15 16:57 -0500
              Re: Toughest Game Show Question Kaz Kylheku <kaz@kylheku.com> - 2012-01-16 04:16 +0000
                Re: Toughest Game Show Question gazelle@shell.xmission.com (Kenny McCormack) - 2012-01-16 12:14 +0000
                Re: Toughest Game Show Question Bill Reid <hormelfree@gmail.com> - 2012-01-17 07:31 -0800
                Re: Toughest Game Show Question Tim Rentsch <txr@alumni.caltech.edu> - 2012-01-26 09:33 -0800
    Re: Toughest Game Show Question "BartC" <bc@freeuk.com> - 2012-01-12 21:07 +0000
      factor jgk@panix.com (Joe keane) - 2012-01-12 22:53 +0000
      Re: Toughest Game Show Question pete <pfiland@mindspring.com> - 2012-01-14 23:38 -0500

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