I believe I found the solution but would like a confirmation. The probability of a certain event $A$ happening is $0.375$. One way to calculate is the event not happening is to take the complement of $A$. So:
$$\bar{A} =1 - 0.375 = 0.625$$

If we wanted to find the probability of an event not happening after **exactly** (key word exactly) $k$, we can multiply $\bar{A}$, $k$ times then subtract our result from $1$.

For example, let us find the probability of event $A$ finally happening after exactly $8$ times.

$$0.625^8 \implies 0.0232 \implies 1 - 0.0232 \implies 0.9768 \implies 97.68\% $$

Is my solution correct?