When a terrible event produces widespread fear, it is often because of the availability heuristic. A tragic event becomes so public, and so memorable, that people feel at risk whether or not they really are.
The second problem is that for some risks, we tend to focus mostly on the possible outcome, and not so much on the likelihood that it will actually come to fruition. Much of the time, of course, we really care about probability. If you are asked how much you would pay to buy a 1 percent chance of winning $500, you will say a lot less than if you are asked how much you would pay to buy a 99 percent chance of winning $500.
But when people's emotions are running especially high, the outcome is the dominant consideration, and it can crowd out consideration of probability. Studies show that when people are asked how much they would pay to avoid a 1 percent chance of getting a painful electric shock, their answer is only slightly lower than what it is when they are asked how much they would pay to avoid a 99 percent chance of getting such a shock.
The lesson is straightforward. In situations that trigger strong negative emotions, people tend to focus on the very worst that might happen, and the question of probability turns out to be secondary. Those who sell life insurance exploit this feature of human nature. You might be able to persuade people to buy insurance if you can get them to think about the economic risks faced by their family.
When terrorists succeed in generating widespread fear, it is also because they get people to focus on terrible outcomes, and not on the likelihood that they will come about. Because strong emotions are produced by the prospect of a terrorist attack, people might well become more frightened than reality warrants.