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Re: Toughest Game Show Question

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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.

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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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