You are playing a simplified version of darts. For each throw, you choose one of two distances from the target and throw the dart. If you hit the target from the short distance, you get 2 points, and if you hit it from the long distance, you get 3 points. You get no points for missing the target.
You get N throws, and you must get at least W points to win. You hit the target with probability P1 percent from the short distance, and with probability P2 percent from the long distance. Return the expected probability (as a percentage between 0 and 100) that you will win.