Probability
Total Probability — Ball Transfer Between Bags
nta_pyq_2026_jan
Grade 12
Question:
Bag A contains 9 white and 8 black balls, while bag B contains 6 white and 4 black balls. One ball is randomly picked 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 $\dfrac{p}{q}$, $\gcd(p,q)=1$, then $p+q$ is equal to
Step-by-Step Solution
Key Concept: Case 1: White transferred from B ($P=\tfrac{6}{10}$). A becomes 10W+8B. $P(\text{white})=\tfrac{10}{18}=\tfrac{5}{9}$. Case 2: Black transferred ($P=\tfrac{4}{10}$). A becomes 9W+9B. $P(\text{white})=\tfrac{9}{18}=\tfrac{1}{2}$.
$P(\text{white})=\tfrac{8}{15}$. $p+q=23$.
Correct Answer: 1