From: srw@horus.ps.uci.edu (Steven White)
Subject: Re: Marilyn Vos Savant's error?
Newsgroups: sci.math,rec.puzzles
Reply-To: srw@horus.ps.uci.edu (Steven White)
Organization: University of California, Irvine
Distribution: na
Date: 5 Jan 93 00:19:59 GMT

In article <1993Jan2.215958.1@stsci.edu>, zellner@stsci.edu writes:
|> Steve White (srw@horus.ps.uci.edu) 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


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