NetNews Usenet Archive 1992 #31/NN_1992_31.iso/spool/alt/folklore/science/4494

Internet Message Format | 1992-12-24 | 3.6 KB

Path: sparky!uunet!news.claremont.edu!nntp-server.caltech.edu!SOL1.GPS.CALTECH.EDU!CARL
From: [e-mail] (Carl J Lydick)
Newsgroups: alt.folklore.science
Subject: Re: More Monty Hall
Date: 24 Dec 1992 19:22:04 GMT
Organization: HST Wide Field/Planetary Camera
Lines: 56
Distribution: world
Message-ID: <[e-mail]>
References: <[e-mail]> <[e-mail]> <[e-mail]> <[e-mail]>,<[e-mail]>
Reply-To: [e-mail]
NNTP-Posting-Host: sol1.gps.caltech.edu

In article <[e-mail]>, [e-mail] (Dennis Worden) writes:
>Now reword the situation a little:
>After Monty opens the door with the goat behind it, he then asks you to
>choose between the remaining two doors, one with the prize, and the other
>with the goat.  You have a 50% chance of picking the correct one (remember,
>the third door does not exist in the wording).  You have a 50% chance
>of picking the correct door here.  You have the same information as before,
>the only change is that instead of asking you to "switch", you are asked
>to "pick from start".  Either way, you have two doors in front of you,
>and one prize.

Sorry, but Monty wasn't allowed to pick just any door.  He wasn't allowed to
pick the one YOU chose.  Hence his choice was constrained.  This is NOT the
same as allowing Monty to reveal a goat before you ever pick a door.

>This is the same as tossing a coin; what are the chances of it coming up
>heads: 50%.  Toss it again, and what is the chance of it coming of heads?
>Still 50%.  The fact that it came up heads previously does not affect this
>toss.  Monty hasn't given you new information, he has given you a new
>question.  At the point where he asks you if you want to switch, the fact
>that you had a 33% chance previously doesn't affect you new decision; two
>doors, one prize.
>
>The fallacy here is assigning the 33% chance from the door Monty opened
>totally to the last door.  The 33% distributes across both door, afterall,
>just because you now know the prize isn't behind one of the doors, doesn't
>tell you where it is.

But Monty wasn't free to choose the door you opened.  That biases the odds in
favor of the door you opened having a goat.

>That 33% chance splits evenly between the remaining
>two doors, and you have 50%.  To believe otherwise is the same as saying
>you approach three doors, one of which is open and has a goat, two of
>which are closed.

Well, if you'd be so stupid as to sometimes pick the one that's open and has a
goat, then you're correct.  You would, however, be one of the few people so
stupid.

>Whichever door you pick only has a 33% chance of being
>right, the other door has a 67% chance of being correct.  Now that doesn't
>make any sense does it?

No, it doesn't.  But you're discussing an entirely different problem.  In a
previous post, I enumerated the possible outcomes, along with probabilities for
each.  Why not try addressing that enumeration of the problem rather than
arguing by extremely flawed analogy?
--------------------------------------------------------------------------------
Carl J Lydick | INTERnet: [e-mail] | NSI/HEPnet: SOL1::CARL

Disclaimer:  Hey, I understand VAXen and VMS.  That's what I get paid for.  My
understanding of astronomy is purely at the amateur level (or below).  So
unless what I'm saying is directly related to VAX/VMS, don't hold me or my
organization responsible for it.  If it IS related to VAX/VMS, you can try to
hold me responsible for it, but my organization had nothing to do with it.