JEE Main 2026 (Online) 23rd January Evening ShiftQuestion 1
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 the bag $B$ and mixed up with the balls in the bag $A$. Then a ball is randomly drawn from the bag $A$. If the probability that the ball drawn is white is $\frac pq$, where $\gcd(p,q)=1$, then what is the value of $p+q$ ?
Probability
Solution
$P=\frac{6}{10}\cdot\frac{10}{18}+\frac{4}{10}\cdot\frac{9}{18}=\frac{8}{15}$, so $p+q=23$.