Good decisions account for risks. For example, the risk of an accident while driving in the rain makes a reasonable driver decide to slow down. While risk is a large topic in theoretical disciplines such as economics and psychology, as well as in practical disciplines such as medicine and finance, philosophy has a unique contribution to make in developing a normative theory of risk that states what risk is, and to what extent our responses to it are rational.Weirich here develops a philosophical theory of the rationality of responses to risk. He first distinguishes two types of risk: first, a chance of a bad event, and second, an act's risk in relation to its possible outcomes. He argues that this distinction has normative significance in the sense that one's attitudes towards these types of risks - and how one acts on them - are governed by different general principles of rationality. Consequently, a comprehensive account of risk must not only characterize rational responses to risk but also explain why these responses are rational. Weirich explains how, for a rational ideal agent, the expected utilities of the acts available in a decision problem explain the agent's preferences among the acts. As a result, maximizing expected utility is just following preferences among the acts. His view takes an act's expected utility, not just as a feature of a representation of preferences among acts, but also as a factor in the explanation of preferences among acts.The book's precise formulation of general standards of rationality for attitudes and for acts, and its rigorous argumentation for these standards, make it philosophical; but while mainly of interest to philosophers, its broader arguments will contribute to the conceptual foundations of studies of risk in all disciplines that study it.