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Personal decisions about health hazards are the main cause of impaired health and premature death. People smoke and eat too much, and they exercise too little. The lack of preventive efforts is surprising given their proven effectiveness. In the early 1960s, Arrow suggested that moral hazard might be a reason for underprevention, but this explanation was later challenged. In this paper, we show that underprevention might be caused by misperceived probabilities. We derive when and how probability weighting gets in the way of prevention by blurring its benefits. We use a general model of prevention, encompassing several special cases from the literature. We also show how perceived ambiguity makes the problem of underprevention even worse by amplifying the effect of probability weighting.