We document two new facts about the distributions of answers in famous statistical problems: they are i) multi-modal and ii) unstable with respect to irrelevant changes in the problem. We offer a model in which, when solving a problem, people represent each hypothesis by attending “bottom up” to its salient features while neglecting other, potentially more relevant, ones. Only the statistics associated with salient features are used, others are neglected. The model unifies biases in judgments about i.i.d. draws, such as the Gambler’s Fallacy and insensitivity to sample size, with biases in inference such as under- and overreaction and insensitivity to the weight of evidence. The model makes predictions about how changes in the salience of specific features should jointly shape the prevalence of these biases and measured attention to features, but also create entirely new biases. We test and confirm these predictions experimentally. Bottom-up attention to features emerges as a unifying framework for biases conventionally explained using a variety of stable heuristics or distortions of the Bayes rule.