Answer
$\frac{14}{15}$
Work Step by Step
For mutually exclusive events, $P(S\text{ and }T) = 0$, so we have $$\begin{aligned}
P(S\text{ or }T)& = P(S) + P(T) - P(S\text{ and }T) = P(S) + P(T)\\
$P(S\text{ or }T)& =\frac{3}{5} + \frac{1}{3}\\
& = \frac{9}{15} + \frac{5}{15}\\
& = \frac{14}{15}.
\end{aligned}$$
