An experiment consists of selecting a point $(x, y)$ from the interior of the unit circle, $x^2 + y^2 < 1$.
(a) What fraction of the points in the space satisfy $x > \frac{1}{2}$?
(b) What fraction of the points in the space satisfy $x^2 + y^2 > \frac{1}{2}$?
(c) What fraction of the points in the space satisfy $x + y > \frac{1}{2}$?
(d) What fraction of the points in the space satisfy $x + y = \frac{1}{2}$?