On the provenance of judgments of conditional probability

Abstract

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(notA∩B)] fared better (Experiment 2).


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