On the provenance of judgments of conditional probability

Jiaying Zhao, Anuj Shah, Daniel Osherson

Research output: Contribution to journalArticle

16 Scopus citations

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 (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.

Original languageEnglish (US)
Pages (from-to)26-36
Number of pages11
JournalCognition
Volume113
Issue number1
DOIs
StatePublished - Oct 2009

All Science Journal Classification (ASJC) codes

  • Experimental and Cognitive Psychology
  • Language and Linguistics
  • Developmental and Educational Psychology
  • Linguistics and Language
  • Cognitive Neuroscience

Keywords

  • Conditional probability
  • Judgment
  • Reasoning

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