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Probabilistic risk assessment attempts to predict the frequency of occurrence of hypothetical events by the development and analysis of a mathematical-logic model of the generative physical system. The discipline involves an amalgam of probability theory and engineering, as in reliability analysis, combined with a concern for psycho-social, medical and economic issues, due to the public-policy aspect of many applications. The literature in the field has the superficial appearance of well reasoned, dispassionate analysis extrapolated to its logical implications. However, critical examination reveals unresolved social and theoretical issues of fundamental importance. These matters are discussed from both a mathematical and a socioeconomic perspective. From consideration of socioeconomic dynamics, it is argued that, notwithstanding the great difficulty of the problem and serious limitations of current risk assessment procedures, advanced technological civilization requires some form of prospective risk/benefit analysis.