Reasoning and inference are well-studied aspects of basic cognition that have been explained as statistically optimal Bayesian inference. Using a simplified experimental design, we conducted quantitative comparisons between Bayesian inference and human inference at the level of individuals. In 3 experiments, with more than 13,000 participants, we asked people for prior and posterior inferences about the probability that 1 of 2 coins would generate certain outcomes. Most participants' inferences were inconsistent with Bayes' rule. Only in the simplest version of the task did the majority of participants adhere to Bayes' rule, but even in that case, there was a significant proportion that failed to do so. The current results highlight the importance of close quantitative comparisons between Bayesian inference and human data at the individual-subject level when evaluating models of cognition.