Abstract: When strong emotions are triggered by a risk, people show a remarkable tendency to neglect a small probability that the risk will actually come to fruition. Experimental evidence, involving electric shocks and arsenic, supports this claim, as does real-world evidence, involving responses to abandoned hazardous waste dumps, the pesticide Alar, and anthrax. The resulting "probability neglect" has many implications for law and policy. It suggests the need for institutional constraints on policies based on ungrounded fears; it also shows how government might effectively draw attention to risks that warrant special concern. Probability neglect helps to explain the enactment of certain legislation, in which government, no less than ordinary people, suffers from that form of neglect. When people are neglecting the fact that the probability of harm is small, government should generally attempt to inform people, rather than cater to their excessive fear. But when information will not help, government should respond, at least if analysis suggest that the benefits outweigh the costs. The reason is that fear, even if it is excessive, is itself a significant problem, and can create additional significant problems.