The current study investigates whether preschoolers are able to successfully identify the most effective among given questions, adapting their reliance on different types of questions ("constraint-seeking" vs. "hypothesis-scanning") based on the quantitative measure of "expected information gain." Children were presented with storybooks describing the reasons why a fictional character, Toma, was late to school over several days. In 3 experiments with 5-year-old children, we manipulated the frequency and likelihoods of the reasons presented. Children were asked to identify which of 2 given questions would be more effective in finding out why Toma was late to school again. In a fourth experiment, we investigated whether preschoolers are "adaptive" learners, that is, whether they can identify the most effective question iteratively, and we extended our investigation to younger preschoolers (3- and 4-year-olds). We find that children assessed the effectiveness of different types of questions based on the hypothesis space currently under consideration, and this adaptation may be guided by expected information gain. Overall, our results suggest that over the preschool years, children begin to develop the computational foundations that support successful question-asking strategies.