A Geometry and Probability Simulation
- Steve Phelps
From Brilliant.org https://brilliant.org/community-problem/an-intersection-of-geometry-and-combinatorics/?group=mioNVQMD8KUE. Consider a square with vertices (0,0) and (1,0). Choose a random point within the square and draw a line segment from it to (0,0). Next, choose a second random point within the square and draw a line segment from this point to (1,0). The probability that these two line segments intersect is , where and are positive coprime integers. Find the probability. Each trial consists of generating 100 random segment pairs and counting the number of segments pairs that intersect. Each dot in the dot plot represents the number of segment pairs intersections in each trial.