Geometric Experimental Probability: Polygon Sampling and Theory vs Practice

This GeoGebra example demonstrates how theoretical probability can be approximated experimentally by repeatedly sampling random points inside geometric regions and checking how many land in a target set. It connects probability with planar geometry and visualizes the gap and convergence between theoretical probability and empirical estimates. The key mathematical ideas are theoretical vs experimental probability, random experiments, and geometry-based probability via region membership (a point-in-region criterion). Construction-wise, it uses Polygon to build the main polygonal regions (e.g., using points P1–P4 and boundary segments segmAB, segmBC, segmCD, segmDA and others), PointIn to test whether a generated point belongs to the intended region (objects q1, q2 together with points like peep, A–H), Zip to combine/organize point collections into pointsList, and CountIf to count accepted points (pointsIn, countIn). The app updates outputs such as probTheo/currentProb and the corresponding text labels (probTheoText, probText) while button1/button2 control the sampling workflow. Suitable for secondary school through early undergraduate learning, especially for teaching probability & statistics with geometric modeling and computational experiments.