Given that the events $A$ and $B$ are such that $P(A) = \frac{1}{2}$,$P(A \cup B) = \frac{3}{5}$,and $P(B) = p$. Find $p$ if they are mutually exclusive.
- A$\frac{1}{10}$
- B$\frac{2}{5}$
- C$\frac{1}{5}$
- D$\frac{3}{10}$
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