Confirm that the probability for a random line in a square to be the diagonal of a square contained in the square is 2/3; see https://math.stackexchange.com/questions/2906823.

Question2906823.java

public class Question2906823 {
	final static int ntrials = 100000000;
	public static void main (String [] args) {
		int count = 0;
		
		for (int n = 0;n < ntrials;n++) {
			double x1 = Math.random ();
			double y1 = Math.random ();
			double x2 = Math.random ();
			double y2 = Math.random ();
			double mx = (x1 + x2) / 2;
			double my = (y1 + y2) / 2;
			double dx = x1 - mx;
			double dy = y1 - my;
			double xa = mx + dy;
			double ya = my - dx;
			double xb = mx - dy;
			double yb = my + dx;
			if (inRange (xa) && inRange (ya) && inRange (xb) && inRange (yb))
				count++;
		}
		
		System.out.println (count / (double) ntrials);
	}
	
	static boolean inRange (double x) {
		return 0 <= x && x <= 1;
	}
}