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The Europa mission approved in 2019 is still in the development phase. It is designed to conduct a detailed reconnaissance of that moon of Jupiter as it could possibly support life as we know it. This article is based on a top-down approach (mission → system → subsystems → components) to model the probability of mission failure. The focus here is on the case where the (uncertain) radiation load exceeds the (uncertain) capacity of critical subsystems of the spacecraft. The model is an illustrative quantification of the uncertainties about (1) the complex external radiation environment in repeated exposures, (2) the effectiveness of the shielding in different zones of the spacecraft, and (3) the components' capacities, by modeling all three as dynamic random variables. A simulation including a sensitivity analysis is used to obtain the failure probability of the whole mission in forty-five revolutions around Jupiter. This article illustrates how probabilistic risk analysis based on engineering models, test results and expert opinions can be used in the early stages of the design of space missions when uncertainties are large. It also describes the optimization of the spacecraft design, taking into account the decisionmakers' risk attitude and the mission resource constraints.