Coupon Collector's Problem: How Many Dice Rolls to See All Faces?

① This GeoGebra example dynamically simulates rolling a die to illustrate the Coupon Collector's Problem—how many rolls are needed to collect all six faces with high probability. ② Core mathematical concepts include expected value, probability distributions, random simulation, frequency statistics, and the law of large numbers, focusing on the expectation of a discrete random variable and its convergence. ③ Construction highlights: using GeoGebra commands such as Unique, Length, Frequency, Sum, Mean, TableText, Sequence, and PolyLine to track distinct outcomes and plot cumulative frequency curves; multiple buttons (button1, button2, button3) control single roll, batch rolls, and auto-run; sliders (a, b, c, d) adjust parameters; dynamic text objects display current roll count and collected faces. ④ Suitable for high school to undergraduate probability and statistics courses, as well as math lab activities or inquiry-based learning, helping students connect theoretical expected values with empirical simulation results and appreciate computational verification of mathematical concepts.