Acircleof radius r is a curve that consists of all points at distance r from the center of the circle.

Adiskof radius r is the set of all points whose distance from its center isless than or equalto r.

(a). We generate a random circle of radius 1, whose center is uniformly distributed inside a disk of radius 10 centered at the origin; see figure above.

Find the probability that the random circle intersects a circle of radius r=5, also centered at the origin. (Give a numerical answer.)

(b). Answer the same question as in Part (a) but for the case where r, instead of being 5, is the realized value of a random variable R that is uniformly distributed between 2 and 5. (Give a numerical answer.)