From: carl@SOL1.GPS.CALTECH.EDU (Carl J Lydick)
Newsgroups: rec.puzzles
Subject: Re: Are you sure? YES <SPOILER>
Date: 26 Jan 1993 13:42:09 GMT
Organization: HST Wide Field/Planetary Camera
Distribution: world
Reply-To: carl@SOL1.GPS.CALTECH.EDU
NNTP-Posting-Host: sol1.gps.caltech.edu

In article <1993Jan26.115545.11556@eng.cam.ac.uk>, cmh@eng.cam.ac.uk (C.M. Hicks) writes:
=karr@cs.cornell.edu (David Karr) writes:
=
=>>You meet the daughter of a friend of yours on the street.  You know
=>>that your friend has two children.  You think to yourself, "Ignoring
=>>the occurrence of twins, and sex-linked differences in birth rates
=>>and infant mortality, what are the odds of this girl's sibling also
=>>being a girl?"
=
=One half - The probability of the other child being a girl is totally
=independent of the sex of the first. The first child being
=a girl does affect the 50-50 boy-girl distribution of the second (or any 
=other) child.
=
=Even if your friend had 10 children, and you met nine of them in the street,
=all girls, then the probability of the tenth being female is still one half.
=
=Of course, the probability of having ten girls is 1/1024 (assuming no
=genetic oddities), but the probability of any one child being a girl is
=one half

OK, maybe if we do this by enumeration, it'll convince people.  Suppose there
are four families.  One has two boys, one two girls, one has an older boy and
youger girl, and the fourth has an older girl and younger boy.  Are you agreed
that each of these four possibilities is equally likely?  Now, suppose as
you're walking around, you run into each of these children separately.  Are you
agreed that the odds of meeting them are identical?  If so, then we have the
following equiprobably possibilities:

Description of child you meet		Gender of sibling
--------------------------------	-----------------
Oldest boy from first family		Male
Youngest boy from first family		Male
Oldest girl from second family		Female
Youngest girl from second family	Female
Boy from third family			Female
Girl from third family			Male
Boy from fourth family			Female
Girl from fourth family			Male

Each of these is equally likely.  Now we note that the problem speficies that
you met a girl.  The possibilities here are:

Description of child you meet		Gender of sibling
--------------------------------	-----------------
Oldest girl from second family		Female
Youngest girl from second family	Female
Girl from third family			Male
Girl from fourth family			Male

Thus there's a 50% chance that the sibling is female.  This is *NOT* the same
as the "I've got two children and at least one of them is a girl" question. 
--------------------------------------------------------------------------------
Carl J Lydick | INTERnet: CARL@SOL1.GPS.CALTECH.EDU | NSI/HEPnet: SOL1::CARL

Disclaimer:  Hey, I understand VAXen and VMS.  That's what I get paid for.  My
understanding of astronomy is purely at the amateur level (or below).  So
unless what I'm saying is directly related to VAX/VMS, don't hold me or my
organization responsible for it.  If it IS related to VAX/VMS, you can try to
hold me responsible for it, but my organization had nothing to do with it.
Newsgroups: rec.puzzles