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From: 6850150@LMSC5.IS.LMSC.LOCKHEED.COM
Subject: Re: 3-prisoners problem
Message-ID: <17036B76ES86.6850150@LMSC5.IS.LMSC.LOCKHEED.COM>
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Organization: Lockheed Missiles & Space Company, Inc.
References:  <35cp8v$a8n@ixnews1.ix.netcom.com>
Date: Mon, 19 Sep 1994 20:02:30 GMT
Lines: 43

In article <35cp8v$a8n@ixnews1.ix.netcom.com>
jhc@ix.netcom.com (James Conklin) writes:
 
>
>In <359fi2$kmg@canopus.cc.umanitoba.ca> umholme0@cc.umanitoba.ca (Douglas Alan Holmes) writes:
>
>>
>>In <35609e$917@ixnews1.ix.netcom.com> jhc@ix.netcom.com (James Conklin) writes:
>>
>>>As soon as you find out that one of the choices not taken is a losing chose
>>>the probability that the one you have already picked goes up to 1/2.
>>>It does so because you have obtained more information about the system.
>>
>>Use the same logic picking the Ace of Hearts from a deck of cards. Choose
>>one card but don't look. Then have someone throw out 50 cards from the
>>deck and leave one and they tell you that one of the two cards is the
>>Ace. By your logic, you will have the Ace 1/2 the time.
>>
>>The extra information would change the odds if you knew it before you
>>chose, but is not retroactive.
>>
>>
>
>You will have the Ace 1/2 of the time if and only if the ace is one of the
>two cards left.  Note that on most of the tries where someone has thrown
>out the 50 cards they will have thrown out the Ace.
 
If, however, you chose a card and the dealer throws out fifty cards that are
*known to not be the Ace*, then the probability that you have the Ace is still
one in fifty two.
You chose the card with a one in 52 probability of it being The Ace.
Fifty cards are identified to Not Be The Ace. They are set aside.
The dealer holds one card. Your odds of having the Ace are 1 in 52, and that
was your original likelihood of selecting the Ace. If you are allowed to choose
between the card you selected (which you still have not viewed) and the dealerz
card, knowing that one of the two is the Ace, your likelihood of choosing the
Ace is increased to 1/2.
I was certain that Marilyn Von Savant was wrong with her Monty Hall proof. Upon
working it out, though, I learned that she was correct. The "Deck of Cards"
metaphor makes it far more clear, though, that the option of resellecting will
increase one's odds of success.
regards
vjm
