When presented with 2 samples (a smaller sample from a Minority population and a larger sample from a Majority population), where some rare or frequent features occur at exactly the same rate in both samples, people reliably associate the rare feature with the Minority population and the frequent feature with the Majority population. This pattern is referred to as "illusory correlation," reflecting the standard assumption that such associations are fundamentally irrational. In this article we show that this assumption is incorrect, and demonstrate that this pattern of association linking rare features with the Minority and frequent features with the Majority (given a sample where those features occurred at the same proportion in both categories, and no further information) is in fact correct and follows a result in epistemic probability theory known as the "Rule of Succession." Building on this result, we present a new computational model of frequency-based illusory correlation, based on the Rule of Succession. We also discuss the implications of the Rule of Succession for our understanding of various other cognitive biases.