For the joint density $$f_{xy}\left(xy\right) = x + \frac{3}{2}y^{2};0\leq x \leq 1,0 \leq y \leq 1$$, the value of $$P\left(0 \leq Y \leq \frac{1}{2}\mid 0 \leq X \leq \frac{1}{2}\right)$$ is:

A

$$\frac{8}{32}$$

B

$$\frac{6}{32}$$

C

$$\frac{10}{32}$$

D

$$\frac{12}{32}$$