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Re: The "two child problem"




Marilyn's answer is correct, for reasons several others have already given
in detail.

However, I'm surprised Marilyn didn't suggest that each reader can test
this. Just throw two coins one after the other. The fall of the coin
represents the outcome of a birth, male or female.

What is the probability that the *first* one thrown (the oldest) is a
head?

What is the probability that *at least one* of the coins is a head?

Doubting readers could repeat the coin experiment as often as they like
and tally the results.

Even in the case of twins, one is always recorded as being born first.
Also, I'm sure Marilyn wasn't concerned with the slight difference in
male/female birth rates, which, in this case, wouldn't be enough to affect
the conclusion she specifically asked for.

-- Donald

......................................................................
Dr. Donald E. Simanek Office: 717-893-2079
Prof. of Physics Internet: dsimanek@eagle.lhup.edu
Lock Haven University, Lock Haven, PA. 17745 CIS: 73147,2166
Home page: http://www.lhup.edu/~dsimanek FAX: 717-893-2047
......................................................................


On Mon, 28 Jul 1997, John Mallinckrodt 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