Queries about singular causation face two problems: It needs to be decided whether the two observed events are instantiations of a generic cause-effect relation. Second, causation needs to be distinguished from co-incidence. We propose a computational model that addresses both questions. It accesses generic causal knowledge either on the individual or the group level. Moreover, the model addresses the possibility of a coincidence by adopting Cheng and Novick’s (2005) power PC measure of causal responsibility. This measure delivers the conditional probability that a cause is causally responsible for an effect given that both events have occurred. To take uncertainty about both the causal structure and the parameters into account we embedded the causal responsibility measure within the structure induction (SI) model developed by Meder et al. (2014). We report the results of three experiments that show that the SI model better captures the data than the power PC model.