Judging Unlikely Conjunctions
Several procedures were used to elicit direct numerical estimates of the probabilities associated with various events created by the conjunction of three independent subevents. However the question was asked, many respondents showed a misunderstanding of the conjunction rule. Less than one half met the minimal criterion of consistently assigning a probability to the conjunction that was no larger than that associated with the least likely constituent event. As a result, subjects as a whole greatly overestimated the conjunctive probability. When attention was restricted to individuals who had followed the conjunction rule, a tendency remained to overestimate the smallest probabilities, relative to the calculated values. Subsidiary results concerned the effects on judgment of wishful thinking, the similarity of the constituent events, and the source of the constituent events. The implications of these results for eliciting and presenting the probabilities of unlikely events are also discussed.