In daily life, probabilities are often assessed informally through the perceived distance to a target event. Accident probabilities are believed to be high when a disastrous outcome appears to be close. This proximity heuristic can lead to exaggerated p(death) estimates in risky situations (Experiment 2), and sometimes higher probabilities for death after near-accidents than after actual accidents (Experiment 3 and 4). Near-accidents are also believed to be equally good, or better, predictors of future disasters than actual accidents, despite being less serious and more frequent (Experiment 5). The proximity heuristic influences the way people talk about their own and other people's chances (Experiment 1), and how they prepare to avoid (or, if necessary, to produce) a disastrous outcome (Experiment 6).