Compared kindergartners', third graders', and undergraduates' understanding and attribution of randomness. Found that kindergartners' interpretations were deterministic or outside the determinancy-indeterminancy frame. Most third graders had some grasp of randomness; their interpretations were less dominated by false attribution of determinism than kindergartners'. Undergraduates also showed performance deficiencies, suggesting that interpreting random phenomena constitutes a nontrivial challenge even for adults. (Author/KB)