Probability of Being Struck by Lightning

Date: Wed, 23 Aug 1995 15:19:22 -0400
From: Pat Vennebush
Subject:  Probability problem

Dear Dr. Math,

   OF the 3.4 million secretaries in the US, 39,000 are male.  While
all 3.4 million secretaries were at the annual secretaries' day
picnic, a vicious storm began.  Lightning headed directly for the
secretaries.  Given that males are eight times as likely to be hit by
lightning as females, what is the probability that one of the male
secretaries will be struck?

   (Of course, this problem assumes that the lightning will indeed
hit one of the attendees, and not a tall tree or a metal flagpole. 
Also, let me say that both of these facts are true:  only 39,000 of
the 3,400,000 secretaries in the US are male--or so Business Week
says--and an article several years ago in _Men's Health_ titled "The
Gender Gap" stated that men are eight times as likely to be hit by
lightning.)

   Anyway, looking forward to hearing from ya, doc.

Sincerely,
Patrick Vennebush
MATHCOUNTS Curriculum Coordinator

Date: 8/23/95 at 15:35:10
From: Doctor Ken
Subject: Re:  Probability problem

Hello there!

Well, I just got your question a second ago, and I just can't resist 
replying right away, because as a man, I want to figure out the answer!
The way you can use the "eight times as likely" information is to say that
for every man at the convention, there are seven additional "virtual" men
standing there beside them to proxy for them in case of lightning.  So the
effective number of male secretaries at the convention is eight times the 
actual number, i.e. 39,000 * 8 = 312,000 male secretatries.  This also 
changes the total number of secretaries at the convention, so we can add 
the number of female secretaries to this new number, and get 
3,361,000 + 312,000 = 3,673,000 which is our new total number of 
secretaries.  Now we just divide:  312,000/3,673,000 = .0849, the 
probability that a man will be struck.  Compare that with the value you'd 
get if men were equally likely to get struck: 39,000/3,400,000 = .0115, 
which is more than one-eighth of the other probability: the probability
went up less than eight-fold with the additional information from
Men's Health.

-Doctor Ken,  The Geometry Forum