In the land of Puzzlevania, Aaron, Bob, and Charlie had an argument over which one of them was the greatest puzzler of all time. To end the argument once and for all, they agreed on a duel to the death. Aaron was a poor shooter and only hit his target with a probability of 1/3. Bob was a bit better and hit his target with a probability of ½. Charlie was an expert marksman and never missed. A hit means a kill and the person hit drops out of the duel.

To compensate for the inequities in their marksmanship skills, the three decided that they would fire in turns, starting with Aaron, followed by Bob, and then by Charlie. The cycle would repeat until there was one man standing, and that man would be the Greatest Puzzler of All Time.

An obvious and reasonable strategy is for each man to shoot at the most accurate shooter still alive, on the grounds this shooter is the deadliest and has the best chance of hitting back.

Write a Java application to simulate the duel using this strategy. Your application should use random numbers and the probabilities given in the problem to determine whether a shooter hits the target. Create a class named Dueler that contains the dueler's name and shooting accuracy, a boolean indicating whether the dueler is still alive and a method shootAtTarget(Dueler target) that sets the target to dead if the dueler hits his target (using a random number and the shooting accuracy) and does nothing otherwise.

Once you can simulate a single duel, add a loop to your application that simulates 1,000 duels. Count the number of times that each contestant wins and prints the probability of winning for each contestant (ie., for Aaron, your application might output "Aaron won 395/1,000 duels or 39.5%").