Re: The "two child problem"

[Maurice Barnhill <mvb@UDel.Edu>]

Clarence Bennett wrote:
> > There are four possible cases for two children (oldest listed first):
> > 1. SS
> > 2. SD
> > 3. DS
>
> > In the case of the woman we have less information, and the
> information
> > is exhausted by saying that we have case 1, 2, or 3.  In the absence
> of
> > further information any of the three cases is equally likely, and
> since
> > two of the cases involve an additional son and one doesn't,
>
> But also, two of the cases include a daughter, and one doesn't.
>
> I think I'm back to even, and the herring was red.
>
> (Except for Martha's entirely separate consideration)
>
> Clarence
> Oakland University
> Rochester, Michigan
> http://www3.acs.oakland.edu/physics/staff_info/Bennett.htm

and of course I got the argument right and the conclusion wrong (*never*
say completely sure).  Of the three cases, one includes 2 sons, and the
chances of the woman having two sons is one in three, *less* than the
man.  Always assuming we are permitted to work only with the information
given.  If in addition one or more children belong to both of them, the
information changes and therefore so does the answer [see how good I am
at weaseling out?].
-- 
Maurice Barnhill, mvb@udel.edu                
http://www.physics.udel.edu/~barnhill/          
Physics Dept., University of Delaware, Newark, DE 19716