Psychological scientists use statistical information to determine the workings of human behavior. We argue that young children do so as well. Over the course of a few years, children progress from viewing human actions as intentional and goal directed to reasoning about the psychological causes underlying such actions. Here, we show that preschoolers and 20-month-old infants can use statistical information-namely, a violation of random sampling-to infer that an agent is expressing a preference for one type of toy instead of another type of toy. Children saw a person remove five toys of one type from a container of toys. Preschoolers and infants inferred that the person had a preference for that type of toy when there was a mismatch between the sampled toys and the population of toys in the box. Mere outcome consistency, time spent with the toys, and positive attention toward the toys did not lead children to infer a preference. These findings provide an important demonstration of how statistical learning could underpin the rapid acquisition of early psychological knowledge.