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JEE Main 202623 JanuaryEvening Shift
Exam
JEE Main
Year
2026
Date
23 January
Shift
Evening Shift
Subject
Mathematics
Chapter
Probability

JEE Main 2026 · 23 January · Evening Shift · Mathematics · Probability

Bag A contains 9 white and 8 black balls, while bag B contains 6...

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

Options

  1. A23
  2. B24
  3. C21
  4. D22

Correct answer

A. 23

Step-by-step solution

Bag A: 9W, 8B. Bag B: 6W, 4B.
Case 1: White transferred from B (prob =610= \frac{6}{10}). A becomes 10W, 8B. P(white from A)=1018=59P(\text{white from A}) = \frac{10}{18} = \frac{5}{9}.
Case 2: Black transferred from B (prob =410= \frac{4}{10}). A becomes 9W, 9B. P(white from A)=918=12P(\text{white from A}) = \frac{9}{18} = \frac{1}{2}.
Total probability =610⋅59+410⋅12=13+15=815= \frac{6}{10} \cdot \frac{5}{9} + \frac{4}{10} \cdot \frac{1}{2} = \frac{1}{3} + \frac{1}{5} = \frac{8}{15}.
p=8,q=15,gcd⁡(8,15)=1p = 8, q = 15, \gcd(8,15) = 1. So p+q=23p + q = 23.
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