This article advances a view of Computer Algebra Systems (CAS) as powerful inquiry-based learning tools. Through an in-depth exploration of the "Emptying the Bowl" activity, upper level mathematics students test their own mathematical hypotheses, thoughtfully analyse and manipulate computer-generated output, and answer questions involving experimental and theoretical probabilities. Throughout the investigation, CAS provides intermediate results rather than "final answers." The unforeseen complexities that underlie "Emptying the Bowl" encourage students (and their teachers) to reconsider connections between early grades and upper level mathematics. (Contains 1 table and 6 figures.)