This article explores the uses of a simulation model (the two bucket story)--implemented by a stand-alone computer program, or an Excel workbook (both on the web)--that can be used for deriving bootstrap confidence intervals, and simulating various probability distributions. The strengths of the model are its generality, the fact that it provides a powerful approach that can be fully understood with very little technical background, and the fact that it encourages an active approach to statistics--the user can see the method being acted out either physically, or in imagination, or by a computer. The article argues that this model and other similar models provide an alternative to conventional approaches to deriving probabilities and making statistical inferences. These simulation approaches have a number of advantages compared with conventional approaches: their generality and robustness; the amount of technical background knowledge is much reduced; and, because the methods are essentially sequences of physical actions, it is likely to be easier to understand their interpretation and limitations.