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.