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Judging two events in combination (A&B) as more probable than one of the events (A) is known as a conjunction fallacy. According to dual-process explanations of human judgment and decision making, the fallacy is due to the application of a heuristic, associative cognitive process. Avoiding the fallacy has been suggested to require the recruitment of a separate process that can apply normative rules. We investigated these assumptions using functional magnetic resonance imaging (fMRI) during conjunction tasks. Judgments, whether correct or not, engaged a network of brain regions identical to that engaged during similarity judgments. Avoidance of the conjunction fallacy additionally, and uniquely, involved a fronto-parietal network previously linked to supervisory, analytic control processes. The results lend credibility to the idea that incorrect probability judgments are the result of a representativeness heuristic that requires additional neurocognitive resources to avoid.