🚀 go-pugleaf

Sean Morgan (morgan@arc.ab.ca) wrote:
: 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?"

Suppose there are just four families.  Each family has two children.
One family has two boys, a second has two girls, and the other two
have one of each.  Denote these families as BB, GG, BG, and GB.

There are four girls, and two of them have sisters.  If you pick
one of the girls at random, then the probability is 1/2 that she
has a sister.

Now suppose you pick one of the mothers at random.  You ask her if
she has at least one daughter, and she says that she does.  The probability
that both of her children are daughters is 1/3.

Do you see why the answers are different?  The woman must belong to
GG, GB, or BG; each of these cases are equally likely.  The girl must
also be a member of GG, GB, or BG; but GG is twice as likely as the
other two cases. 

Let us consider another situation.  Suppose you wish to find the
average family size in a community.  If you pick children at random
and record the number of members of their families, then large families
will be overrepresented.  You would get a more accurate result if
you pick mothers at random.  (I have ignored certain sociological
realities here, of course.)

--
David Radcliffe                                
radcliff@csd4.csd.uwm.edu