People must often make inferences about, and decisions concerning, a highly complex and unpredictable world, on the basis of sparse evidence. An “ideal” normative approach to such challenges is often modeled in terms of Bayesian probabilistic inference. But for real-world problems of perception, motor control, categorization, language comprehension, or common-sense reasoning, exact probabilistic calculations are computationally intractable. Instead, we suggest that the brain solves these hard probability problems approximately, by considering one, or a few, samples from the relevant distributions. By virtue of being an approximation, the sampling approach inevitably leads to systematic biases. Thus, if we assume that the brain carries over the same sampling approach to easy probability problems, where the “ideal” solution can readily be calculated, then a brain designed for probabilistic inference should be expected to display characteristic errors. We argue that many of the “heuristics and biases” found in human judgment and decision-making research can be reinterpreted as side effects of the sampling approach to probabilistic reasoning.