From: jerry@hnrc.tufts.edu (Jerry Dallal)
Newsgroups: bit.listserv.edstat-l
Subject: Re: switcheroo
Date: 4 Oct 92 15:09:25 GMT
Organization: USDA HNRC at Tufts University

In article <9210030426.AA29433@oz.plymouth.edu>, hayden@OZ.PLYMOUTH.EDU (Dr. Robert Hayden) writes:
> 
>           The Saga of J. Laurie Snell
> 
> In the wee hours of Sunday morning, J. Laurie Snell prepares 40
> envelopes.  20 contain $100, and these he puts in the left inside
> pocket of his sports coat.  10 contain $200 and 10 contain $50.  These
> 20 he puts in the right inside pocket of his sportscoat.
> 
> Monday morning he ventures out upon the campus of Dartmouth College.
> He accosts the first 20 people he meets, and hands them one envelope
> randomly selected from his R.I.P. and  one envelope
> randomly selectehd from his L.I.P.  10 people will get (50,100) and 10
> people will get (100,200).
> 
> 
> He then asks them to open one of the envelopes.  If the envelope
> opened contains $50 or $200, he tells them to keep both envelopes and have
> a nice day.  Let us say that half the people who got (50,100) and half
> the people who got (100,200) happened to open the $100 envelope.  To
> these people he says
> 
>       One of the two envelopes contains twice as much as the
>       other.  You may keep either the $100 or the contents of
>       the unopened envelope.  Which do you choose?
> 
> Last Monday, they all chose the $100 and he gave out $2000.  However,
> the week before they all chose the unopened envelope and he gave out
> $2500.
> 
> Questions
> 
> 1. Are there any errors in the arithmetic above?
> 
> 2. Is this problem isomorphic to the Marilyn vos Savant problem?  If
>    not, why not.
> 
> Please make it clear which question you are answering!
> --

            Preamble:  My head is spinning.  Except for the 
        contribution from Albyn Jones, I feel like I've been swimming 
        upstream, responding in a collegial fashion (well, most of the 
        time) to all the nuances raised by the many posters.  I'm 
        trying to hang around to resolve any lingering questions that 
        might remain, and I wouldn't want those of you who've had some 
        insights from the ongoing discussion of this problem to 
        think I had changed my mind if I should stop responding to the 
        onslaught.  But, I'm tired.  Right now, I'm beginning to 
        believe 1 + 1 = 3 (in any base!!!) if someone says it with 
        authority.  So, I may be missing something here and I reserve 
        the right to repost this response *without prejudice*, 
        but . . .
            
            Your arithmetic is correct. 

            This is not the same problem.  You have done by fiat what 
        others are doing subjectively, i.e., you have forced P(50/100 
        game) = P(100/200 game) = 0.5.  In the vos Savant problem, the 
        contents of Snell's RIP are unknown!  (Who is this J. Laurie 
        Snell?  May I take part in the experiment?) 
> 
> 
>       _
>      | |          Robert W. Hayden
>      | |          Department of Mathematics
>     /  |          Plymouth State College
>    |   |          Plymouth, New Hampshire 03264  USA
>    | * |
>   /    |          (603) 536-2497
>  |     )          (603) 535-2489
>  L_____/          hayden@oz.plymouth.edu
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU