Five studies investigated (a) children's ability to use the dependent and independent probabilities of events to make causal inferences and (b) the interaction between such inferences and domain-specific knowledge. In Experiment 1, preschoolers used patterns of dependence and independence to make accurate causal inferences in the domains of biology and psychology. Experiment 2 replicated the results in the domain of biology with a more complex pattern of conditional dependencies. In Experiment 3, children used evidence about patterns of dependence and independence to craft novel interventions across domains. In Experiments 4 and 5, children's sensitivity to patterns of dependence was pitted against their domain-specific knowledge. Children used conditional probabilities to make accurate causal inferences even when asked to violate domain boundaries.