We propose a normative model of inductive reasoning about causal arguments, those in which there is a direct causal relation between categories. The model derives inductive judgments from a causal Bayesian network that represents the causal structure of the argument. It supports inferences in the causal direction (e.g. a mother is drug-addicted, how likely is it that her newborn baby is drug-addicted?), and in the diagnostic direction (e.g. a newborn baby is drug-addicted, how likely is it that the babys mother is drug-addicted?). We explored how causal and diagnostic judgments should change as a function of the parameters of the model, which include the prior probability of the cause, the causal power of the cause to bring about the effect, and the strength of alternative causes. The model was fit to the results of an experiment in which we manipulated the strength of alternative causes by varying the predicate while keeping the categories constant. Contrary to the predictions of previous theories, participants were not biased to over-estimate causal judgments relative to diagnostic judgments. Instead, they neglected alternative causes when reasoning causally and hence systematically underestimated causal judgments. Conversely, diagnostic judgments were sensitive to the strength of alternative causes and were unbiased, demonstrating that inductive reasoning is sensitive to some rational principles.