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Data Set #037

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    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.

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Source: Masters, Gilbert M., Introduction to Environmental Engineering and Science



log(Lifetime Risk)




Cigarette smoking, one pack per day

all cancers


All cancers

motor vehicles


Death in motor vehicle accident

home accidents


Home accident death



Radon in homes, cancer deaths



Alcohol, light drinkers, cancers

background radiation


Sea level background radiation, cancers

peanut butter


4 tablespoons peanut butter per day (aflatoxin)

EPA contaminant (max)


Typical EPA maximum allowable contaminant level (lowest standard)

EPA contaminant (min)


Typical EPA maximum allowable contaminant level (highest standard)


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