Statistics and Probability: JEE Main 2025 Mathematics question

Given three identical bags each containing 10 balls, whose colours are as follows: \\ \textbf{Bag I:} Red = 3, Blue = 2, Green = 5 \\ \textbf{Bag II:} Red = 4, Blue = 3, Green = 3 \\ \textbf{Bag III:} Red = 5, Blue = 1, Green = 4 \\ A person chooses a bag at random and takes out a ball. If the ball is Red, the probability that it is from bag I is $p$ and if the ball is Green, the probability that it is from bag III is $q$, then the value of $\left( \frac{1}{p} + \frac{1}{q} \right)$ is: