Sure, but then, since all the other doors were open, the odds would be 1 in
1.

If, however, the door 777,777 were unopened as well as the one I had, it
would be 1 in 2.  It would also be 1 in 2 that the door I picked originally
would be the correct one.

I will grant you that prior to choosing, the odds are 1 in 1,000,000, but
the second that Monty opened 999,998 doors, the odds that I chose the right
door are now 1 in 2.

This kind of analysis seems to indicate that my odds cannot improve by
decreasing my choices.

-------------------------------------------------------------
Gary L. Paveza, Jr.
Technical Support Specialist

        -----Original Message-----
        From:   Stigers, Greg [And] [SMTP:[log in to unmask]]
        Sent:   Wednesday, March 01, 2000 1:52 PM
        To:     'Paveza, Gary'; 'HP3K-L'
        Subject:        RE: OT: Probability question

        X-no-Archive:yes
        Keep scratching. From
        http://qsilver.queensu.ca/~phil158d/intro/montyh3.htm#prob. There is
a quite
        a bit of information there, including the letter from Robert Sachs,
Ph.D. of
        George Mason University, stating "Please help by confessing your
(Marilyn
        vos Savant) error and in the future being more careful".

        The Monty Hall Problem

        You're on a TV game show. In front of you are three doors: there's a
great
        prize behind one door, and nothing behind the other two. You choose
a door.
        Then the host (Monty Hall) opens one of the two doors you didn't
choose to
        show that there is nothing behind that door. It would be bad for the
TV
        ratings if he opened the prize door: you'd know you had lost and the
game
        would be over; so Monty knows where the prize is, and he always
opens a door
        that doesn't have a prize behind it (Monty is Canadian, so you know
you can
        trust him). You're now facing two unopened doors, the one you
originally
        picked and the other one, and the host gives you a chance to change
your
        mind: do you want to stick with the door you originally chose, or do
you
        want to switch to what's behind the other door?

        Marilyn's answer)
        ...you should switch. The first door has a 1/3 chance of winning,
but the
        second door has a 2/3 chance. Here's a good way to visualize what
happened:
        Suppose there are a million doors, and you pick door number 1. Then
the
        host, who knows what's behind the doors and will always avoid the
one with
        the prize, opens them all except door number 777,777. You'd switch
to that
        door pretty fast, wouldn't you?

        -----Original Message-----
        From: Paveza, Gary [mailto:[log in to unmask]]
        Sent: Wednesday, March 01, 2000 1:38 PM
        To: [log in to unmask]
        Subject: Re: OT: Probability question

        Every time I hear this one I scratch my head in confusion.
        <snip>