Card-Based Visualization of a Probability Distribution

This example demonstrates how to visualize a discrete probability distribution using a “cards/segments” style construction, mapping the same distribution to different geometric layouts such as bar-like and sector/circle-based representations. The key math ideas are discrete probability distribution, allocation/counting with normalization (reflected by vector constructions and summations), and step functions (piecewise constant behavior) to represent probability masses. Construction highlights from the GeoGebra command summary: Sequence generates ordered items; Element selects referenced components; KeepIf filters items using conditions; Mod supports cyclic indexing to distribute cards according to the rule; Sum aggregates the relevant quantities; Vector together with Translate positions the generated “cards” in the plane; and the layout is further connected to rotation/sector/circle visualization in the scene. Suitable for high school through early university learning, especially for teaching discrete probability concepts and using GeoGebra to combine probability with geometric transformations and step-function graphs.