Heterogeneity of subsurface environments and insufficient site characterization are some of the reasons why decisions about groundwater exploitation and remediation have to be made under uncertainty. A typical decision maker chooses between several alternative remediation strategies by balancing their respective costs with the probability of their success or failure. We conduct a probabilistic risk assessment (PRA) to determine the likelihood of the success of a permeable reactive barrier, one of the leading approaches to groundwater remediation. While PRA is used extensively in many engineering fields, its applications in hydrogeology are scarce. This is because rigorous PRA requires one to quantify structural and parametric uncertainties inherent in predictions of subsurface flow and transport. We demonstrate how PRA can facilitate a comprehensive uncertainty quantification for complex subsurface phenomena by identifying key transport processes contributing to a barrier's failure, each of which is amenable to uncertainty analysis. Probability of failure of a remediation strategy is computed by combining independent and conditional probabilities of failure of each process. Individual probabilities can be evaluated either analytically or numerically or, barring both, can be inferred from expert opinion.