A point is chosen at random from the region $S$ in the $xy$-plane containing all points $(x,y)$ such that $-1\le x\le 1, -3\le y\le 3$ and $x - y\ge 0$ (at random means that the density function is constant on $S$).

(a) Determine the joint density function for $x$ and $y$ in $S$
$p(x,y) =$
(with $p(x,y) = 0$ for all $(x,y)$ not in $S$.)

(b) If $T$ is a subset of $S$ with area $a$, find the probability that a point $(x,y)$ is in $T$.
probability =