This paper investigates a fundamental conflict in the literature on people's probability estimation. Research on 'perception' of probability shows that people are accurate in their estimates of probability of various simple events from samples. Equally, however, a large body of research shows that people's probability estimates are fundamentally biased, and subject to reliable and striking fallacies in reasoning. We investigate this conflict in an experiment that examines the occurrence of the conjunction fallacy in a probability perception task where people are asked to estimate the probability of simple and conjunctive events in a presented set of items. We find that people's probability estimates are accurate, especially for simple events, just as seen in previous studies. People's estimates also show high rates of occurrence of the conjunction fallacy. We show how this apparently contradictory result is consistent with a recent model of probability estimation, the ‘probability theory plus noise' model.