Abstract
Joint occurrence, a confusion of a conditional probability P(B|A) with a conjunction probability P(A&B), appears frequently in Bayesian problems. In this study, university students were instructed to rank the following probabilities, P(positive|cancer), P(cancer&positive) and P(cancer| positive) in a thematized problem, by their probability in a written format. 25% of the students answered correctly, P(positive|cancer) > P(cancer|positive) > P(cancer&positive). 38% of the students committed the cognitive fluctuation error (Nakagaki, 2006), that is, they equated the conditional probability P(positive|cancer) with the conjunction probability P(cancer&positive) in the ranking problem. This result is consistent with Itoh's (2008) study in which approximately 40% of university students confused P(B|A) with P(A&B) in a Bayesian drawing-of-lots problem. The results suggest the possibility that conditional probabilities and conjunction probabilities are interpreted as identical.
