A disk of radius 1 meter is drawn on the pavement and both a polar (r,)(r,) and Cartesian coordinate system (x,y)(x,y) are used to label points in the disk, the origin being chosen as the centre of the disk. Suppose raindrops land on the disk in such a way that they are equally likely to fall centred on any specific point on the disk. Answer the following questions justifying your answers.

A) What is the probability that a raindrop that lands in the disk, lands at the point (x,y)=(1/2,1/2)(x,y)=(1/2,1/2)?

B) What is the probability that a raindrop that lands in the disk, lands within a radius of rr of the origin, where 0

C) What is the probability that a raindrop that lands in the disk, lands within a radius of rr of the origin, and in the region where 0<

D) A cover, itself a circular disk of radius R=1/2R=1/2 is placed randomly within the disk so that its perimeter is within the original disk. What is the probability that a raindrop lands in the unprotected area.

E) A raindrop lands at point (x,y)(x,y) in the disk. What is Pr[|x|<|y|]Pr[|x|<|y|].