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 -