Cascading Galton Boards

Children struggle to learn basic ideas of probability distributions and sampling, despite the fact that we see these around us all the time. The Galton Board (see galtonboard.com) is an elegant and intuitive mechanical simulation that makes the origin of Gaussian distributions very clear. But physical Galton Boards are hard to make. Your task is to make a customisable animated simulation - but not just of a single distribution. Users should be able to chain multiple boards together, associating them with descriptive equations, creating a visual probabilistic programming language as a zoomable giant pinball machine that can help teach conditional probability and an intuitive derivation of Bayes theorem.