One aspect of risk assessment involves estimating
the probability of occurrence of a particular event given a certain
set of circumstances. For example, the probability of flipping "heads"
on a fair coin is 0.5 or 50%. There are only two possible outcomes,
heads or tails, and each outcome has an equal likelihood when a fair
coin is used.

Circumstances surrounding some risk must be evaluated
very carefully to understand the meaning or significance of a probability
attached to the risk. For example, 50 people die from bee stings in
the United States each year. The population in the US is approximately
275 million people, suggesting a probability of dying from a bee sting
of approximately 10^{-7}. However, not everyone in the US
is stung by a bee in a year; the pool of potential victims might be
1/10,000 of the total population. The probability of dying from a
bee sting IF you are stung might be as high as 10^{-3}, much
more impressive. When evaluating a probability value, study the circumstances
carefully.

The table gives probabilities for death from various
causes over the lifetime of an individual. Though not stated, it's
likely that some of the risks in the table represent mean probabilities
for both men and women combined (who have different life spans), and
that the population involved is all people in the US. However, it's
very likely that this table represents many different risk studies
done by different researchers, and therefore different populations
may be involved. Motor vehicle accidents often occur at a young
age, creating a problem for the statistician; what does "lifetime
risk" mean if the lifetime is only 25 years?

The values in the table are given as the logarithm
of the probability. In the bee sting example, the probability of US
citizens dying in a year is 10^{-7}; the logarithm is therefore
-7, about the same probability as dying from exposure to a hazardous
substance at a minimal concentration over a lifetime. The risk of
death in smoking a pack of cigarettes a day for life is 10^-0.60 =
0.25 or 25% chance. This is roughly equivalent to shortening a span
by about 5 minutes for each cigarette smoked (Wilson and Crouch, 1987,
as reported by G.M. Masters).

Radon, an odorless and colorless gas that seeps
into homes from the ground, is a radioactive element; one if its daughter
products, bismuth (also radioactive), can lodge in lung tissue and
eventually contribute to lung cancer. A log probability of -2.52 or
a probability of 0.003 implies that over 800,000 people die over 75
years in the US, at a rate of approximately 10,000 people per year.
Radon is believed to be the second leading cause of lung cancer after
smoking. One might ask: how was the original risk of radon-induced
lung cancer determined if the gas is odorless and colorless?

Reference: Based on data given in Wilson and Crouch (1987) and the
Center for Health Statistics. As reported in Masters, G. M., Introduction
to Environmental Engineering and Science, Prentice Hall Publishers,
1991, pp. 192.