Bayesian statistics offers a normative description for how a person should combine their original beliefs (i.e., their priors) in light of new evidence (i.e., the likelihood). Previous research suggests that people tend to under-weight both their prior (base rate neglect) and the likelihood (conservatism), although this varies by individual and situation. Yet this work generally elicits people's knowledge as single point estimates (e.g., x has 5% probability of occurring) rather than as a full distribution. Here we demonstrate the utility of eliciting and fitting full distributions when studying these questions. Across three experiments, we found substantial variation in the extent to which people showed base rate neglect and conservatism, which our method allowed us to measure for the first time simultaneously at the level of the individual. We found that while most people tended to disregard the base rate, they did so less when the prior was made explicit. Although many individuals were conservative, there was no apparent systematic relationship between base rate neglect and conservatism within individuals. We suggest that this method shows great potential for studying human probabilistic reasoning.