A complete quantitative account of P. Wason's (1966) abstract selection task is proposed. The account takes the form of a mathematical model. It is assumed that some response patterns are caused by inferential reasoning, whereas other responses reflect cognitive processes that affect each card selection separately and independently of other card selections. The model parameters assess the contributions of different interpretational, inferential, and heuristic factors that jointly determine performance in the selection task. The interpretation of most of the model parameters in terms of these different factors is validated experimentally. This model of the selection task is the first to account for the observed frequencies of all 16 possible response patterns that can arise.