Conflict detection in dual process contexts is a widely studied phenomenon. However, only a small portion of the investigations has studied the role of individual differences in a typical conflict detection paradigm. In this study, participants completed a modified base-rate neglect task, as well as the Cognitive Reflection Task (CRT), and two Thinking Disposition Questionnaires. Results support an individual differences hypothesis in which the CRT prediction of accuracy on the base-rate conflict problems is mediated by the dispositional tendency to engage in flexible thinking.