Young human learners possess a remarkable ability to make inductive inferences from sparse data. Recent research suggests that childrens generalizations are sensitive to the process by which data are generated (i.e., teacher-driven vs. learner-driven sampling; Xu & Tenenbaum, 2007). In general, sampling process and properties of objects are tightly coupled; knowing how the data were sampled can inform your inference about property extensions, and vice versa. In real-world situations, however, both the extension of novel properties and the sampling process may be ambiguous. These situations commonly arise when children are learning socially from adults. How do children confront the challenge of simultaneously inferring both the property extension and the sampling process from a small amount of data? Here we present a Bayesian model showing how this joint inference problem can be solved. Consistent with the predictions of the model, two behavioral experiments suggest that toddlers (mean: 16 months) can use the relationship between a sample and a population to infer both the sampling process and the extent to which a non-obvious object property should be generalized.