Mathematics · Probability

JEE Main 2026 — 23 January, Evening Shift — Question 11

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 $\frac{\mathrm{p}}{\mathrm{q}}, \operatorname{gcd}(\mathrm{p}, \mathrm{q})=1$ , then $\mathrm{p}+\mathrm{q}$ is equal to

Option A:
22
Option B:
23
Correct
Option C:
24
Option D:
21

Answer: B

Step-by-step solution

Bag $A: 9W, 8B ($ Total $= 17)$ Bag $B: 6W, 4B ($ Total $= 10)$

Case 1: White transferred from B

P = \frac{6}{10}

Bag A becomes: 10W, 8B (Total = 18) $P($ white from $A) = \frac{10}{18}$

Case 2: Black transferred from B

P = \frac{4}{10}

Bag A becomes: 9W, 9B (Total = 18) $P($ white from $A) = \frac{9}{18}$

Total probability:

= \frac{6}{10}\cdot\frac{10}{18} + \frac{4}{10}\cdot\frac{9}{18}

= \frac{1}{3} + \frac{1}{5} = \frac{8}{15}

Thus,

p = 8, \quad q = 15

p+q = \boxed{23}

Answer key and solution verified before publishing.

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Exam: JEE Main 2026
Paper: 23 January, Evening Shift
Subject: Mathematics
Chapter: Probability
Topic: Random Variables, Binomial & Poission Distribution

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