Estimate the probability for n points chosen in/on a circle to lie in/on some semicircle; see http://math.stackexchange.com/questions/325141.

Question325141.java

import java.util.Arrays;

public class Question325141 {
    public static void main (String [] args) {
        int ntrials = Integer.parseInt (args [0]);
        int n = Integer.parseInt (args [1]);

        double [] a = new double [n];

        int count = 0;
        
        for (int i = 0;i < ntrials;i++) {
            for (int j = 0;j < n;j++)
                a [j] = Math.random ();
            Arrays.sort (a);
            
            for (int j = 0;j < n;j++) {
                double diff = a [j] - a [(j + 1) % n];
                if (diff < 0)
                    diff++;
                if (diff < 0.5) {
                    count++;
                    break;
                }
            }
        }

        System.out.println (count / (double) ntrials);
    }
}