Probability and risk

Once we understand that “personal judgment of how likely” and “what happens in many repetitions” are different ideas, we have a good start toward understanding why the public and the experts disagree so strongly about what is risky and what isn’t. The experts use probabilities from data to describe the risk of an unpleasant event. Individuals and society, however, seem to ignore data. We worry about some risks that almost never occur while ignoring others that are much more probable.

EXAMPLE 9 Asbestos in the schools

High exposure to asbestos is dangerous. Low exposure, such as that experienced by teachers and students in schools where asbestos is present in the insulation around pipes, is not very risky. The probability that a teacher who works for 30 years in a school with typical asbestos levels will get cancer from the asbestos is around 151,000,000. The risk of dying in a car accident during a lifetime of driving is about 15,0001,000,000. That is, driving regularly is about 1000 times more risky than teaching in a school where asbestos is present.

Risk does not stop us from driving. Yet the much smaller risk from asbestos launched massive cleanup campaigns and a federal requirement that every school inspect for asbestos and make the findings public.

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image What are the odds? Gamblers often express chance in terms of odds rather than probability. Odds of A to B against an outcome means that the probability of that outcome is B(A + B). So “odds of 5 to 1” is another way of saying “probability 16.” A probability is always between 0 and 1, but odds range from 0 to infinity. Although odds are mainly used in gambling, they give us a way to make very small probabilities clearer. “Odds of 999 to 1” may be easier to understand than “probability 0.001.”

Why do we take asbestos so much more seriously than driving? Why do we worry about very unlikely threats such as tornadoes and terrorists more than we worry about heart attacks?

Our reactions to risk depend on more than probability, even if our personal probabilities are higher than the experts’ data-based probabilities. We are influenced by our psychological makeup and by social standards. As one writer noted, “Few of us would leave a baby sleeping alone in a house while we drove off on a 10-minute errand, even though car-crash risks are much greater than home risks.”