The conjunction fallacy occurs when people judge the conjunctive probability P(A ∧ B) to be greater than a constituent probability P(A), contrary to the norms of probability theory. This fallacy is a reliable, consistent and systematic part of people's probability judgements, attested in many studies over at least 40 years. For some events, these fallacies occur very frequently in people's judgements (at rates of 80% or more), while for other events, the fallacies are very rare (occurring at rates of 10% or less). This wide range of fallacy rates presents a challenge for current theories of the conjunction fallacy. We show how this wide range of observed fallacy rates can be explained by a simple model where people reason according to probability theory but are subject to random noise in the reasoning process.