Estimate the probability of a certain inequality being satisfied for uniformly distributed random variables; see https://math.stackexchange.com/questions/4859023.

Question4859023.java

public class Question4859023 {
    final static long ntrials = 100000000L;
    
    public static void main(String [] args) {
        long count = 0;
        
        for (long n = 0;n < ntrials;n++) {
            double x1 = 5 * Math.random();
            double x2 = 5 * Math.random();
            double y1 = 5 * Math.random();
            double y2 = 5 * Math.random();
            
            if ((x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1) > (x2 + x1) * (x2 + x1))
                count++;
        }
        
        System.out.println(count / (double) ntrials);
    }
}