Mathematics Question from JEE Main 2026 · 23 January, Shift 2

Bag A contains $9$ white and $8$ black balls, while bag B contains $6$ white and $4$ black balls. One ball is randomly picked up from bag B and mixed up with the balls in bag A. Then a ball is randomly drawn from bag A. If the probability that the ball drawn is white is $\frac{p}{q}$, $\gcd(p, q) = 1$, then $p + q$ is equal to