8. Consider the Buffon needle experiment. A horizontal plane is ruled with parallel lines spaced D cm apart. A needle of length d em (d < D) is dropped randomly on the plane.

The objective of the experiment is to determine the probability that either end of the needle touches or crosses one of the lines. Define h = Perpendicular distance from the needle center to a (parallel) line e = Inclination angle of the needle with a line

(a) Show that the needle will touch or cross a line only if h :=5 ~sin 8, 0 ::; h ::; D,o :=5 8 :=5 'IT 2 2