Acceptance-Rejection Sampling

Suppose we want to sample from the PDF of $X \sim \text{Beta}(3,2)$, which has PDF $f(x) = 12x^2(1-x)I_{(0,1)}(x)$. Since you know how to generate uniformly random pairs in the rectangle $R_a = [0,1] \times [0,a]$ for some $a > 0$, you decide to sample from $R_a$. You will count your random point $(X,Y) \in R_a$ as valid for the PDF if it lies in the region bounded by the $x-$axis and $f(x)$. Otherwise, it is rejected. If $a$ is selected to minimize the number of rejected pairs of points per sample, find the expected amount of rejected pairs per accepted pair.