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19 October, 2017
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Risk Assessment and Fermi Problems

Risk Assessment often requires us to estimate probability of a threat for which there is no public information. Here's how to approach the problem.

When I was studying for my Cambridge University entrance exams, one thing was certain. Every year the Physics paper would contain a question like:

What is the probability that the next breath you take contains at least one molecule from Caesar’s last gasp?

This is not, of course, an answer that can be gleaned from a text book. There is (as far as I know) no learned treatise on the last breaths of famous historical characters. The challenge was to make reasonable assumptions, use what you did know, and estimate as well as you could what you didn’t. For example, in the above question you might not know the number of air molecules in the world, but you might be able to estimate it from the earth’s diameter and the approximate thickness of its atmosphere. (Don’t know the thickness of the atmosphere? Then perhaps you can work from the air pressure at ground level and the value of g instead).

I always enjoyed this type of a question, but never realized it was called a Fermi Problem until I listened to a recent BBC Material World podcast. The name comes from the Italian physicist Enrico Fermi who was renowned for his ability to make such estimates. (He estimated the approximate size of the first nuclear explosion from the distance falling pieces of paper were displaced by the shock wave: he estimated the equivalent of 10 kTons of TNT; the actual value was 19 kTons).

Estimating risk is often all about Fermi Problems. We normally don’t have a convenient comparable historical record and must therefore make intelligent assumptions and deductions from the data we do have available.

Here’s a mixed bag of questions you might like to try:

  • How many piano tuners are there in Chicago. (This is the classic example question, with one suggested answer here).
  • How many birds are eaten by domestic cats in the UK each year?
  • How many birds will die through collision with wind farm turbines each year? (Here’s a reference to a detailed assessment for the effect of wind farms on a rare parrot species which you can use to check your assumptions and reasoning).
  • What is the probability of your office building being destroyed by fire next year? (Hint: check your answer by looking at your building’s insurance premium. Unless you have an incompetent insurer this should provide an upper bound on the estimate.)
  • How could you determine the height of your building with a barometer? (This does not require much knowledge of physics although it can help: see if you can find a method not included in Nils Bohr’s classic answer.)
  • How many laptops are likely to be lost or stolen from your company next year?
  • In America, how likely is an employee to die due during a terrorist incident? Due to a homicide? A suicide? A road accident? From a medical problem? (Use the Internet to look for relevant statistics. The CDC has lots of useful statistics for the USA).
  • Which has the greater risk (=probability x impact) for a major city such as New York, a flu pandemic or a major terrorist attack?
  • If Santa delivers presents to all children who believe in Santa, only delivers presents during the night of Christmas Eve, and can travel at the speed of light, what is the upper limit on the number of children who believe in Santa? (Tip: assume that Santa consumes all the cookies that people leave out for him. Your children might also enjoy checking Santa’s progress at NORAD.)

There are no perfect answers to these questions. The objective is to get the right order of magnitude in the result. This is typically sufficient to determine priorities and to determine the allocation of resources.

Have fun!

Michael Z. Bell
December, 2008

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