NetNews Usenet Archive 1993 #1/NN_1993_1.iso/spool/sci/math/17665

Internet Message Format | 1993-01-04 | 3.7 KB

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From: [e-mail] (Steven White)
Subject: Re: Marilyn Vos Savant's error?
Nntp-Posting-Host: horus.ps.uci.edu
Message-ID: <[e-mail]>
Newsgroups: sci.math,rec.puzzles
Reply-To: [e-mail] (Steven White)
Organization: University of California, Irvine
Lines: 84
References: <[e-mail]> <[e-mail]> <[e-mail]> <[e-mail]> <[e-mail]> <[e-mail]> <[e-mail]>
Distribution: na
Date: 5 Jan 93 00:19:59 GMT

In article <[e-mail]>, [e-mail] writes:
|> Steve White ([e-mail]) writes:
|>
|>   > You forgot to label your table. You wanted it to be
|>
|>   >    Older   Younger
|>   >    -----   -------
|>   >    Boy   -   Boy
|>   >    Boy   -   Girl
|>   >    Girl  -   Boy
|>   >    Girl  -   Girl
|>
|> Correct.
|>
|>   > Then your logic seems to hold. But if I label the table:
|>
|>   >    Kid             Kid
|>   > Over there       Elsewhere
|>   >   -----          -------
|>   >   Boy         -   Boy
|>   >   Boy         -   Girl
|>   >   Girl        -   Boy
|>   >   Girl        -   Girl
|>
|> Yes, you could of course do that, but it would be a different problem, and
|> free of the apparent paradox:  Given that at least one of the kids is a boy,
|> the probability of two boys depends on your knowledge of whether the one you
|> see is the elder, the younger or simply "one of them."
|>
|>   >  Then case A gives probability 1/2 and case B gives 1/3.
|>   >  In other words, this argument fails. Neither wording is the
|>   >  same as "at least one of them is a boy".
|>
|>Sorry, you lost me there.  If the man says "one of them is over there", and I
|> look and see a boy, isn't that the same as "at least one of them is a boy"?

No. You know that at least one of them is a boy, but you also know that
the one over there is a boy--ruling out 2 cases in my table.

|>
|> Now then:  Suppose a woman gets pregnant out of wedlock, and decides to give
|> up the child for adoption straight from the delivery room, without even knowing
|> its sex.  A year later, she does it again.  But in later years the rascal who
|> kept getting her pregnant had a change of heart and married her and settled down
|> to be a good husband and father, and they began to wonder about those two
|> childen.
|>
|> Information about adopted children is tightly guarded in some jurisdictions, so
|> they hired a private detective to see what he could find out.  Suppose after
|> some investigation he reported:
|>
|>    "I've found the older child, and it's a boy."
|>
|> Or instead,
|>
|>   "I've found one of the children, and it's a boy, but the records I've been
|>    able to peek at so far don't give its age, so I don't know whether it's
|>    the older or the younger."
|>
|> In each of the two cases, what's the probability that both children are boys?
|> It seems intuitive that the age of the child that he found wouldn't matter, but
|> mathematically it does.  That's the paradox.

Baloney. What's mathematically significant about age? It's just a way of
labeling the kids. Suppose I know that one is a redhead and one is a blond.
Now the p.i. says:

"I've found the older child, and it's a boy. However, I don't know if it's
the redhead."

Or instead,

"I've found the redhead, and it's a boy, but I don't know whether he's
older than the other kid."

Or instead,

"I've found the older kid, and he's a boy and the redhead."

What do you say is the prob. that both are boys? I say it's always 1/2.

                    Steve White