Beliefs and Bayesian reasoning.

We examine whether judgments of posterior probabilities in Bayesian reasoning problems are affected by reasoners' beliefs about corresponding real-world probabilities. In an internet-based task, participants were asked to determine the probability that a hypothesis is true (posterior probability, e.g., a person has a disease, given a positive medical test) based on relevant probabilities (e.g., that any person has the disease and the true and false positive rates of the test). We varied whether the correct posterior probability was close to, or far from, independent intuitive estimates of the corresponding 'real-world' probability. Responses were substantially closer to the correct posterior when this value was close to the intuitive estimate. A model in which the response is a weighted sum of the intuitive estimate and an additive combination of the probabilities provides an excellent account of the results.