Q1: Centroid and Random Experiments in Geometric Probability

① This GeoGebra example dynamically demonstrates the generation of random points inside a triangle and the construction of related points and polygons using the centroid (barycenter) concept, visually linking random experiments with geometric probability. ② Core mathematical concepts include centroid (barycenter), binomial distribution, random experiments, complex numbers, frequency distribution, vector operations, and dynamic coordinates. ③ Construction highlights: using commands such as Intersect, Segment, Point, Sequence, DynamicCoordinates, Polygon, If, and Vector, it creates objects D, E, F, k, j, A, B, C1, VPoints, uCopy, C, f, g, C2, vCopy, UPoints, C', h, G, d, t1, closed1, v, u, text1, i, t3, l, m, n, G', closed2, t2. Random point sets are generated via dynamic coordinates and sequences, while vector copying and conditional logic build closed shapes. ④ Suitable for high school to university students studying probability and statistics, geometric construction, and dynamic mathematics experiments, useful for exploring the relationship between random point distributions and centroid positions, as well as simulating binomial and frequency distributions.