Crossing the River as a Probability Model: Trig Functions and Elliptic Symmetry

This example models a “crossing the river” (roller derby style) game using random experiments and visualizes how success conditions translate into point distributions and statistical summaries. It focuses on key ideas such as probability & statistics (random sampling, counting successes, estimating outcomes), function-based decision regions (using conditional logic), trigonometric relationships and symmetry (constraints that induce symmetric structure), and ellipse-related geometric boundaries/trajectories. Construction highlights include using Max and If to compute conditional values, Random to generate samples, CountIf to count points meeting the criterion, Sequence together with Element to build and retrieve parameterized data, and Sort to organize results. Textfield and Text are used for interactive parameter input and reporting, while DotPlot creates the scatter/empirical distribution. A variety of GeoGebra objects (including variables and interactive buttons) coordinate the dynamic updates. Suitable for middle/high school and introductory college courses to connect probability simulation with trig/geometric function graphs and symmetry.