This article proposes a novel framework for understanding judgments of probability. Both accurate and inaccurate judgments are conceptualized in terms of the sets of information, or sample spaces, on which they are based. When appropriate sample spaces are easily accessed from memory (e.g., when they correspond to natural cognitive categories), people will make relatively accurate judgments; otherwise, people may substitute more accessible but inappropriate sample spaces and make judgment errors. In 3 experiments, the sample space framework was applied to account for the base rate fallacy. Results showed that (a) people spontaneously access sample spaces that correspond to natural categories, (b) reliance on inappropriate sample spaces produces the base rate fallacy, and (c) highlighting appropriate sample spaces improves the sensitivity of people's judgments to base rates. Discussion extends the framework to explain accuracy and error in other judgment domains.