A 1.0-mm-diameter sphere bounces back and forth between two walls at x = 0 mm and x = 100 mm. The collisions are perfectly elastic, and the sphere repeats this motion over and over with no loss of speed. At a random instant of time, what is the probability that the center of the sphere is
a. At exactly x = 50.0 mm?
b. Between x = 49.0 mm and x = 51.0 mm?
c. At x ≥ 75 mm?