If $$p(x) = \begin{cases}{\frac{x}{15};} & x = {1, 2, 3, 4, 5}\\0;& elsewhere\end{cases}$$, the probability $$P\left\{\frac{1}{2} < X < \frac{5}{2}\right\}$$ is equal to:

A

$$\frac{2}{5}$$

B

$$\frac{3}{5}$$

C

$$\frac{4}{15}$$

D

$$\frac{1}{5}$$