Can young children discriminate impossible events, which cannot happen in reality, from improbable events, which are unfamiliar but could possibly happen in reality? When asked explicitly to categorize these types of events, 4-year-olds (N = 54) tended to report that improbable events were impossible, consistent with prior results (Shtulman & Carey, 2007). But when presented with stories made up of improbable events, children preferred to continue these stories with additional improbable events rather than with impossible events, demonstrating their sensitivity to the difference between the two types of events. Children were indifferent between continuing these stories with additional improbable events or with ordinary, possible events. Children's differential performance on the story and categorization tasks suggests that they possess some knowledge of the distinction between improbable and impossible but find it difficult to express this knowledge without a supportive context. (Contains 2 tables.)