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 15/1,000,000. The risk of dying in a car accident during a lifetime of driving is about 15,000/1,000,000. 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.
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 1/6.” 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?
• We feel safer when a risk seems under our control than when we cannot control it. We are in control (or so we imagine) when we are driving, but we can’t control the risk from asbestos or tornadoes or terrorists.
• It is hard to comprehend very small probabilities. Probabilities of 15 per million and 15,000 per million are both so small that our intuition cannot distinguish between them. Psychologists have shown that we generally overestimate very small risks and underestimate higher risks. Perhaps this is part of the general weakness of our intuition about how probability operates.
• The probabilities for risks like asbestos in the schools are not as certain as probabilities for tossing coins. They must be estimated by experts from complicated statistical studies. Perhaps it is safest to suspect that the experts may have underestimated the level of risk.
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.”