TY - JOUR

T1 - On the provenance of judgments of conditional probability

AU - Zhao, Jiaying

AU - Shah, Anuj

AU - Osherson, Daniel

N1 - Funding Information:
Thanks to Steven Sloman and David Over for helpful comments on an earlier version of this manuscript. Three anonymous referees also provided valuable input. Osherson acknowledges support from the Henry Luce Foundation. Contact information: jiayingz/akshah/[email protected] .

PY - 2009/10

Y1 - 2009/10

N2 - 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.

AB - 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.

KW - Conditional probability

KW - Judgment

KW - Reasoning

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U2 - 10.1016/j.cognition.2009.07.006

DO - 10.1016/j.cognition.2009.07.006

M3 - Article

C2 - 19665110

AN - SCOPUS:70349974973

SN - 0010-0277

VL - 113

SP - 26

EP - 36

JO - Cognition

JF - Cognition

IS - 1

ER -