On the provenance of judgments of conditional probability

In standard treatments of probability, Pr(A|B) is defined as the ratio of Pr(A∩B) to Pr(B), provided that Pr(B)>0. This account of conditional probability suggests a psychological question, namely, whether estimates of Pr(A|B) arise in the mind via implicit calculation of Pr(A∩B)/Pr(B). We tested this hypothesis (Experiment 1) by presenting brief visual scenes composed of forms, and collecting estimates of relevant probabilities. Direct estimates of conditional probability were not well predicted by Pr(A∩B)/Pr(B). Direct estimates were also closer to the objective probabilities defined by the stimuli, compared to estimates computed from the foregoing ratio. The hypothesis that Pr(A|B) arises from the ratio Pr(A∩B)/[Pr(A∩B)+Pr(A¯∩B)] fared better (Experiment 2). In a third experiment, the same hypotheses were evaluated in the context of subjective estimates of the chance of future events.