🚀 go-pugleaf

In <1992Dec22.185741.9823@berlioz.nsc.com> worden@bouncer.nsc.com (Dennis Worden) writes:


[kitten's words deleted for space]

>The fact that you now have an open door with a goat behind it does not
>change the fact that you have 2 door and 1 prize.  The opening of the
>third door only tells you that the prize is not behind that door, it does
>not add any information as to where the prize really is.  Or put it another
>way, if you consider this new information on the same puzzle, why do you
>freeze the probability of the original guess at 33%?  To freeze the original
>probabilities at their "pre-new-information" levels means that your are not
>using that new information.  The new information would apply equally to all
>doors that are left, and adjusts the probability to 50%.  The original
>assumption of 33% chance per door was based upon 3 closed doors.  The new
>question is which of 2 closed doors has the prize.


>-- 
>Dennis Worden, not representing $  When the TEAM succeeds, you succeed,
>anybody, not even himself, in   $  but when the Team fails, you're FIRED.
>any way shape or form.          $  Don't EMAIL me at worden@berlioz.nsc.com

  (I know in advance this is likely a waste of time)

  Let's examine all possible cases, okay?  There are three doors, 
which we will designate alpha, beta, and gamma.  The prize is behind
door gamma, so there are three cases, namely, you pick alpha, you 
pick beta, you pick gamma.

   Case alpha:  you have not picked the prize.  Monty reveals the
goat behind beta.  If you switch, you pick gamma and win.

  Case beta:  you have not picked the prize.  Monty reveals the goat
behind alpha.  If you switch, you win.
 
  Case gamma:  you have picked the prize.  Monty reveals either the
goat behind alpha or the one behind beta.  If you switch, you lose.

  Thus, 2/3 of the time, if you switch, you win.  This constitutes
proof by exhaustion.

  (Don't nitpick that there are cases in which the prizes can be behind 
alpha or beta - those cases reduce to simply a renaming of the doors
in my analysis.)


-- 
Carl Fink          carlf@panix.com, C.FINK4(GEnie), or CF427620I@LIUVAX.BITNET
  "Facts are stubborn things; and whatever may be our wishes, our
  inclinations, or the dictates of our passions, they cannot alter
  the state of facts and evidence"     --      John Adams