In some domains, people focus on the goodness or badness of an outcome, without giving sufficient thought to the likelihood that the outcome will actually come to fruition. Neglect of probabilities is especially likely when strong emotions are triggered by a risk; in such cases, people's concern does not greatly vary despite large variations in the probability of harm. 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 bears on the legality of agency action under the many statutes that require agencies to attend to the magnitude of the risk that they seek to address, and also to balance benefits against costs. Indeed, the emerging law of judicial review shows an incipient appreciation of probability neglect and appears to have created a presumption that this form of neglect is unlawful. Probability neglect also helps to explain the enactment of certain legislation. 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 suggests 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.