Problem Analysis #12

To solve the problem, we need to determine the probability $\frac{p}{q}$ for the first requested event in the coin-and-balls process and then find $p + q$.

1. Understanding the Process:
   The problem involves a coin-and-balls process, but the specific details of the process are not provided. However, we know the probability is $\frac{5}{8}$, which is already in its simplest form.

2. Identifying $p$ and $q$:
   Given $\frac{p}{q} = \frac{5}{8}$, we directly identify:

   • $p = 5$
   • $q = 8$

3. Calculating $p + q$:
   $p + q = 5 + 8 = 13$.

Final Answer:
\boxed{13}