For standard statistical problems, we provide new evidence documenting i) multi-modality and ii) instability in probability estimates, including from irrelevant changes in problem description. The evidence motivates a model in which, when solving a problem, people represent each hypothesis by attending to its salient features while neglecting other, potentially more relevant, ones. Only the statistics associated with salient features are used. 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 for how changes in the salience of specific features jointly shapes known biases and measured attention to features, but also create entirely new biases. We test and confirm these predictions experimentally. Salience-driven attention to features emerges as a unifying framework for biases conventionally explained using a variety of stable heuristics or distortions of the Bayes rule.