Conjunction Fallacy

What is the Conjunction Fallacy?

The conjunction fallacy occurs when someone judges two events occurring together as more probable than one of those events occurring on its own. For the same information and possible outcomes, P(A and B) cannot exceed P(A) or P(B). This rule does not require the events to be independent.

Tversky and Kahneman (1983) studied cases in which a detailed combination appeared more plausible or representative than its broader category. A familiar example compares “bank teller” with “bank teller and active in the feminist movement.” Everyone in the second group is also in the first.

The useful check is simple: is one possibility entirely contained in the other? If so, the narrower possibility cannot be more probable. Wording and presentation matter: formats that make the subset relationship clear can reduce errors.

The base-rate fallacy concerns neglecting general prevalence information when judging a particular case.