Although even infants appear to consider multiple possibilities, preschoolers often fail tasks that require reasoning about mutually exclusive alternatives. We review two explanations for this failure: (1) children have a minimal representation of possibility and fail to distinguish necessary from merely possible outcomes; and (2) children are sensitive to this distinction, but competing motivations (e.g., the tendency to explore) can lead to apparent failures. To test these hypotheses, we assessed 3- and 4-year-olds on a novel search task. Here, children searched for an object that was dropped from either a transparent (one necessary location) or opaque (two possible locations) set of inverted Y-shaped tubes. In Exp. 1, we found that children spent less time searching the first location when there were two possible candidates. Exp. 2 replicates these results in a digital task that does not require manual search.