A point $(x, y)$ is to be selected from the square $S$ containing all points $(x, y)$ such that $0 \leq x \leq 1$ and $0 \leq y \leq 1$. Suppose that the probability that the selected point will belong to each specified subset of $S$ is equal to the area of that subset. Find the probability of each of the following subsets: ${}{}$
(a) the subset of points such that $(x - \frac{1}{2})^{2} + (y-\frac{1}{2})^{2} \geq \frac{1}{4}$;
(b) the subset of points such that $\frac{1}{2} < x + y < \frac{3}{2}$,
(c) the subset of points such that $y \leq 1 - x^{2}$;
(d) the subset of points such that $x = y$.