Thus it was written in the epistle of Paveza, Gary,
> Every time I hear this one I scratch my head in confusion.
>
> At the beginning, you have a 1 in 3 chance of guessing the right door.
>
> You choose,  Monty always opens one door.  There are two doors remaining
> (including the one you choose).  You now have a 1 in 2 chance of having the
> right door.
>
> If you choose the other, you still have a 1 in 2 chance of having the right
> door.
>
> Now, if you choose the right one the first time and Monty said "CONGRATS",
> then I'd be more inclined to believe you.

Gary,
  What's going on is that Monty knows something and is giving you information.
If you picked a door and then Monty randomly opened one other door, not knowing
what was behind it, that would be different.  In that case, there would be a
1/3 chance that he would open the door with the "Big Deal" behind it.  Of the
remaining 2/3's cases, you'd have already picked the right door 1/2 the time,
so your chances would indeed be 1 in 2.
  But Monty *never* opens the door with the "Big Deal" behind it.  That changes
things.  Let's play a different game.  We bring you into a room with just one
door.  We tell you that two thirds of the time there is a prize behind the
door.  Your choices are
  1) Open the door.  If the prize is there, you get it.  Otherwise you lose.
  2) Lock the door.  If the prize was there, you missed out.  Otherwise, you
     win.
Which would you choose?  Why to open the door, of course.  2/3's of the time,
you win.
  Now let's play this game.  We bring you into a room with two doors.  We tell
you that two thirds of the time there is a prize behind one of the two doors.
Furthermore, we tell Monty which door the prize is behind.  Before you make any
choice, he walks over and opens the other door.  Now you can either open the
remaining door or you can lock it.  Obviously this is the same game.  So your
strategy is the same.
  So now let's go back to the original game.  You pick a door.  Now you have
a game which is identical to game two (and, once Monty opens his door, to game
one).  One third of the time the prize is behind your door.  Two thirds of the
time it's behind one of the other two doors.  Monty opens whichever of those
doesn't contain it.  The probability is 2/3's that it is behind the remaining
door.

Have I confused you sufficiently yet?
Ted
--
Ted Ashton ([log in to unmask]), Info Sys, Southern Adventist University
          ==========================================================
The longer mathematics lives the more abstract -- and therefore, possibly
also the more practical -- it becomes.
                                      -- Bell, Eric Temple (1883-1960)