Probability weighting is a major concept for accommodating systematic departures from expected utility theory. We examine the relation between probability weighting and cognitive ability with two experiments: one recruiting subjects with a large variation in cognitive ability and the other using the within-subject manipulation of time constraints in lottery choices and cognitive tests. We find a significant association between likelihood insensitivity—the cognitive component of probability weighting—and cognitive limitation such that subjects with a lower cognitive score or more interrupted cognition due to time pressure respond less discriminately to intermediate probabilities and more over-sensitively to extreme probabilities. Our findings shed light on the sources of anomalous choices against expected utility theory.