From: seyyed@wuee1.wustl.edu (Seyyed Mahdavian)
Subject: Re: Physics-1A Question (pardeh bardAriye ostAd az mo'ammA)
Organization: Washington University, St. Louis Mo.
Date: Thu, 8 Oct 1992 07:00:11 GMT

In article <ld73c3INNjqj@exodus.Eng.Sun.COM> smortaz@handel.Eng.Sun.COM (Shahrokh Mortazavi) writes:

>i posted the following question a few days ago:
>
>--------
>there are three doors.  behind one of the doors is a prize. 
>you choose a door randomly, say door # 1.  (but dont open it).
>i open one of the other two doors, say door #2, and show you that 
>there is no prize behind it.
>at this point, i give you the choice of changing your mind
>and picking another door (#3), or staying with your original
>choice (#1).  
>
>question: should you change your mind (pick #3) or stick with your
>original choice (#1) ?
>--------

And now ladies and gentlemen, here is the final solution by ostAd himself:
(Attention please ... no talking ... no chewing-gum ... sarApA goosh ... )

>imagine there are a hundred doors:
>
> 1							100
>[ ] [p] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] ... [ ]             
>
>and you pick door # 1.  what is the probability of you being
>right (never mind that youre almost always wrong)?  1/100?  
>good!  theres an appliance-grade 4 mhz z80 running in there 
>afterall.
>
>now lets say the prize is behind door #2.  so i open doors
>3 thru 100 and show you that theres no prize behind them.
>
>so, now we have doors 1 & 2 left, behind one of which there
>is a prize.
>
>if you stay with door #1, youre chances of being right is 
 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
>still only what?  1/100?  very good!  you get a cookie and and a pat
 ^^^^^^^^^^^^^^^^^^^^^^^^
Fascinating!!! Thank you very much for clarifying the problem. You know,
I really had a hard time to understand this part of the problem. I wonder
what would happen to my Farsi and math without vojoude in dAneshmande
bi-nazir. Now that you have beautifully explained the solution, may I
forsat rA moghtanam shemordeh, ask you another short question that is
still bothering me? Thank you in advance for your time and enAyat.
You see, yek Adame nokhAleh asked me: suppose that the prize is behind
the door #1 (but we don't know it of course). The probability that the
prize be behind door #1 is 1/100 right? Now suppose that we open
doors #2 through 100 and show that there is nothing behind it. Knowing
that #2 through 100 are empty, what's the probability that the prize is behind
#1 ? still 1/100 ?!!! I couldn't answer this question, but I am sure
that ostAde mo'azzam will give yek javAbe dandAn shekan be injour
soAlAte moghrezAneh.

>on the head.
>
>if you accept the offer and switch to the remaining door, #2, what
>do you think your chances will be?  think.  98 of the wrong
>choices have been eliminated, and youve been given a chance
>to pick again.  

Another nokhAleh guy came up with the following trick:
He said: I choose #1, but nAgholA yavAshaki wrote on a piece of paper:
"I lied, I chose #2". After you opened #3 through #100, he showed
the paper and said: "kalak zadam! Now what's my best chance?"
lotfan mojAzAte in farde khatAkAr rA ham ta'yin befarmAyid.

Seyyed.

p.s. I knew that you are a better pakhmeh in math rather than in Farsi.
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