Can children solve Bayesian problems, given that these pose great difficulties even for most adults? We present an ecological framework in which Bayesian intuitions emerge from a match between children's numerical competencies and external representations of numerosity. Bayesian intuition is defined here as the ability to determine the exact Bayesian posterior probability by minds untutored in probability theory or in Bayes' rule. As we show, Bayesian intuitions do not require processing of probabilities or Arabic numbers, but basically the ability to count tokens in icon arrays and to understand what to count. A series of experiments demonstrates for the first time that icon arrays elicited Bayesian intuitions in children as young as second-graders for 22% to 32% of all problems; fourth-graders achieved 50% to 60%. Most surprisingly, icon arrays elicited Bayesian intuitions in children with dyscalculia, a specific learning disorder that has been attributed to genetic causes. These children could solve an impressive 50% of Bayesian problems, a level similar to that of children without dyscalculia. By seventh grade, children solved about two thirds of Bayesian problems with natural frequencies alone, without the additional help of icon arrays. We identify four non-Bayesian rules. On the basis of these results, we propose a common solution for the phylogenetic, the ontogenetic, and the 1970s puzzles in the Bayesian literature and argue for a revision of how to teach statistical thinking. In accordance with recent work on infants' numerical abilities, these findings indicate that children have more numerical ability than previously assumed. (PsycInfo Database Record (c) 2021 APA, all rights reserved).