Re: The "two child problem"

["Richard L. Bowman" <rbowman@bridgewater.edu>]

At 08:37 AM 7/28/97 -0800, you wrote:
> Marilyn had previously dealt with the following problem:  A man and a 
> woman each have two children.  The man's older child is a son and at 
> least one of the woman's children is a son.  Is either more likely 
> than the other to have two sons?

Well, here is another two cents worth of ideas on this problem.

I think we have not put enough of emphasis on the independence of one
birth compared to another. Assume that we are considering that the
likelihood of a boy baby being born or a girl baby being born is the same.
(I seem to recall some data indicating that the survivibility or some such
thing is actually slightly different for male and female zygote.)

As soon as we know that one child has been born, the probability of the
other one being a boy is 1/2. In each case above we are looking only at
the possibility of one unknown child being a boy. So the probability is
the same in both cases, i.e. 1/2. The fact that in one case we know the
known child is older is "a red herring".

Richard
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Dr. Richard L. Bowman
Chair, Dept. of Physics                  e-mail:  rbowman@bridgewater.edu
(and Dir. of Academic Computing)                     phone:  540-828-5441
Bridgewater College                                    FAX:  540-828-5479
Bridgewater, VA  22812               http://www.bridgewater.edu/~rbowman/ 
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