Combinatorics and probability: six- to ten-year-olds reliably predict whether a relation will occur

Young children are able to judge which of two possibilities is more likely to occur when these possibilities are characterized by a simple property, like color ("Is it more likely to draw a red chip or a blue chip?"). Here we ask whether they can do so when the possibilities concern a relation between simple properties ("Is it more likely to draw two chips of the same color or two different colored chips?"). Three studies show that from the age of six children are able to predict the occurrence of a relation on the basis of its probability, and that from the age of nine their performance reaches adult levels. These results corroborate the theory of naive extensional reasoning, and are inconsistent with the hypothesis that children need the help of instruction to reason correctly about relations.