NetNews Usenet Archive 1992 #31/NN_1992_31.iso/spool/alt/folklore/science/4439

Internet Message Format | 1992-12-22 | 3.2 KB

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From: [e-mail] (Dennis Worden)
Newsgroups: alt.folklore.science
Subject: More Monty Hall
Message-ID: <[e-mail]>
Date: 21 Dec 92 21:45:59 GMT
References: <[e-mail]> <[e-mail]> <[e-mail]> <[e-mail]>
Sender: worden@bouncer (Dennis Worden)
Distribution: usa
Organization: National Semiconductor Corporation
Lines: 48


>The initial odds that you guessed right are 33%, as your first guess is
>random.  That means there's a 67% chance the prize is between one of the
>other 2 doors.  Now Monty always reveals a "goat" door, so this gives you
>*new* information, the prize is not behind the "goat" door he reveals.  Since
>your initial guess is still 33% at being correct (revealing the goat does
>NOT tell you anything about your door as Monty can *always* reveal a goat)
>this means the remaining door is 67% at being correct.

>Or change the rules a little.  After you pick a door, Monty, instead of
>revealing a "goat", offers a choice of switching your door for BOTH the other
>doors, but you then have to give Monty a "goat".  Do you switch?

>This actually works out to be the same game, just described differently.

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.

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.  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.  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?


--
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 [e-mail]