Answer
$\dfrac{14}{15}$ or approximately $93.3\%$
Work Step by Step
Use the formula for mutually exclusive events to find the probability of the events not happening at the same time.
The formula is $P(S$ $or$ $T)=P(S)$ $+$ $P(T)$.
We have $P(S)=\dfrac{3}{5}$ and $P(T)=\dfrac{1}{3}$.
Plug the values into the formula:
$P(S$ $or$ $T)$ = $\dfrac{3}{5}$ $+$ $\dfrac{1}{3}$
$P(S$ $or$ $T)$ = $\dfrac{9}{15}$ $+$ $\dfrac{5}{15}$
$P(S$ $or$ $T)$ = $\dfrac{14}{15}\approx93.3\%$