# Question

A sharpshooter is aiming at a circular target with radius 1. If we draw a rectangular system of coordinates with its origin at the center of the target, the coordinates of the point of impact, (X, Y), are random variables having the joint probability density

Find

(a) P[(X,Y) ϵ A], where A is the sector of the circle in the first quadrant bounded by the lines y = 0 and y = x;

(b) P[(X,Y) ϵ B], where B = {(x, y)| 0< x2 + y2 < 1/2 }.

Find

(a) P[(X,Y) ϵ A], where A is the sector of the circle in the first quadrant bounded by the lines y = 0 and y = x;

(b) P[(X,Y) ϵ B], where B = {(x, y)| 0< x2 + y2 < 1/2 }.

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