1) Think Area. You'll have to define a maximum area, assuming your carnival customers are somewhere in the neighborhood.
2) Area won't quite cut it. The ball is not a point. Only some distance from the rim of the cup will result in entry into the cup. Too close to the rim and it will just bounce off.
3) Getting the ball into the cup won't cut it, either. Too direct a hit is likely to result in the ball bouncing out of the cup.
4) I hope it's obvious that this is not an entirely random process. When trying to impress young women, those creatures known as young men do tend to try really hard to win the giant teddy bear.