# Marilyn Misses One in a Million by Five Percent

Marilyn is Wrong **Copyright © 1998 Herb Weiner. All rights reserved.**
**Ask Marilyn ®** by Marilyn vos Savant is a column in *Parade Magazine*,
published by PARADE, 711 Third Avenue, New York, NY 10017, USA.
According to Parade, Marilyn vos Savant is listed in the
"Guinness Book of World Records Hall of Fame" for "Highest IQ."

In Marilyn's *Parade Magazine* column of July 12, 1998, she claims that if every one of the magazine's 82 million
readers flips a coin 20 (and **only** 20) times, she would expect 82 of them to get 20 heads in a row.

First of all, I wonder where the 82 million readers come from.
Is Marilyn (or *Parade Magazine*) assuming that **every** adult in **every** household that receives *Parade Magazine*
is a reader? Some people in the household may not read the newspaper at all.
My father, who receives *Parade Magazine* with his
newspaper, recycles the magazine without even opening it.
I haven't done any marketing research, but since not every household purchases a Sunday newspaper,
since not every Sunday newspaper includes *Parade Magazine*, and since not every recipient of
*Parade Magazine* reads it,
82 million readers seems somewhat high to me.

## Check your Math, Marilyn

Charlie Kluepfel <ChasKlu@aol.com>
made the following observation:
Marilyn was asked how many tosses of a coin in a row all showing heads
would it take to make the probability of its occurence one in a million.
Marilyn correctly answered 20. This is correct, as the base 2 logarithm of
one million is 19.93, which rounds to 20. The odds of getting heads 20 times
in a row turns out to be 1/1048576, and 20 is an answer good enough in keeping
with the spirit of the question.

Marilyn then stated that "if every one of Parade's 82 million readers flips a
coin 20 times, we would expect only 82 of them to get a consistent string of
20 heads." This is incorrect, as 82,000,000/1048576 is 78.2, so we would
**expect** 78 readers to get heads for each of their first 20 tries at this
(many would be tempted to try longer, but that's cheating). That's 78 -- not
82.

Of course, 82 is within the range of reasonable possibility. As 78 is the
result of a large sample, each having a tiny probability of success, the
distribution of possible outcomes of this grand experiment would be a Poisson
distribution with mean of 78.2 and therefore a standard deviation of the
square root of 78.2, or 8.8. (98% probability that 58 to 99 people get the 20
in a row first shot; over 90% probability of between 64 and 93).

http://www.wiskit.com/marilyn/million.html last updated July 26, 1998 by herbw@wiskit.com