For each real number a with 0 \leq a \leq 1, let numbers x and y be chosen independently at random from the intervals [0, a] and [0,1], respectively, and let P(a) be the probability that
\sin ^{2}(\pi x)+\sin ^{2}(\pi y)>1
What is the maximum value of P(a) ?
Answer Choices
A. \dfrac{7}{12}
B. 2-\sqrt{2}
C. \dfrac{1+\sqrt{2}}{4}
D. \dfrac{\sqrt{5}-1}{2}
E. \dfrac{5}{8}