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 (over(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.