Preschoolers often switch a response on repeated questioning, even though no new evidence has been provided (Krahenbuhl, Blades, & Eiser, 2009). Though apparently irrational, this behavior may be understood as children making an inductive inferrence based on their beliefs about whether intial responses were correct and the knowledgeability of the questioner. We present a probabilistic model of how the questioners' knowledge and biases to be positive should affect inferences. The model generates the qualitative prediction that an ideal learner should switch responses more often following a "neutral query" from a knowledgeable questioner than following queries from an ignorant questioner. We test predictions of the model in an experiment. The results show that four-year-old children are sensitive to questioners' knowledge when responding to a neutral query, demonstrating more switching behavior when the query is provided by a knowledgeable questioner. We conclude by discussing the practical and theoretical implications for cognitive development.