Re: The "two child problem"

[Richard Langer <rlanger@slps.k12.mo.us>]

Marilyn's answer is absolutely correct - she defined the sample, then she
looked at the results.

The man has one of the following
	older son		older son
	younger son	younger daughter

The woman has one of the following
	older son		older son		older daughter
	younger son	younger daugheter	younger son

THAT IS THE SAMPLE!

For the man, there are TWO ways he can have the defined children, and in
ONE way, he has two sons, ergo 50% probability

For the woman, there are THREE ways she can have the defined children, and
in ONE way, she has two sons, ergo 33% probability

This is COUNTER-INTUITIVE, as is the fact that in vacuo, light objects fall
at the same rate (acceleration) as do heavy objects.

In my opinion, Ms. Vos Savant's appeal to her readers to send her data
about their children is a statistically flawed experiment, but should serve
to silence the less Scientifically Sophisticated amongst her readers.

Her IQ is not really relevant - the correctness of the answer is
independent of who first thought of it.
At 08:37 AM 7/28/97 -0800, you wrote:
> I am going to out myself and confess that I look forward each week to 
> the arrival (in the Sunday paper) of "Parade" magazine and of the 
> "Ask Marilyn" column that it contains.  Yesterday's column was the 
> type of gem that keeps me hanging in there through months of 
> otherwise uninterrupted silly nonsense.
>
> 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?
>
> Marilyn's answer was not very popular.  She was supported, however, 
> by an engineer whose job involves assessing the various risks of 
> nuclear power plants.  Predictably, this caused another flurry of 
> outraged letters from readers at least one of whom intended to write 
> the Nuclear Regulatory Commission.
>
> So, as a break from thermal energy, work-energy theorems, and Martian 
> words, let's see if physicists are really any smarter than either 
> Marilyn's readers or than Marilyn herself (who is, after all, "listed in 
> the 'Guinness Book of World Records' Hall of Fame for 'Highest IQ.'")
>
> What's your answer, how would you justify it, and how confident are 
> you that your answer is correct?
>
> John
> -----------------------------------------------------------------
> A. John Mallinckrodt      http://www.intranet.csupomona.edu/~ajm
> Professor of Physics    mailto:ajmallinckro@csupomona.edu
> Physics Department       voice:909-869-4054
> Cal Poly Pomona            fax:909-869-5090
> Pomona, CA 91768-4031   office:Building 8, Room 223
Richard M. Langer                  Gateway High School,
Physics Teacher                    5101 McRee Ave.
rlanger@dtd1.slps.k12.mo.us        St. Louis, MO 63110