Calculate the probability that \(X+Y \leq 2\) for random variables with joint probability density function as in Exercise 51.

Data From Exercise 51

Calculate \(P(0 \leq X \leq 2 ; 1 \leq Y \leq 2)\), where \(X\) and \(Y\) have joint probability density function

\[p(x, y)= \begin{cases}\frac{1}{72}(2 x y+2 x+y) & \text { if } 0 \leq x \leq 4 \text { and } 0 \leq y \leq 2 \\ 0 & \text { otherwise }\end{cases}\]