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JEE Main 202529 JanuaryEvening Shift
Exam
JEE Main
Year
2025
Date
29 January
Shift
Evening Shift
Subject
Mathematics
Chapter
Probability

JEE Main 2025 · 29 January · Evening Shift · Mathematics · Probability

Bag 1 contains 4 white balls and 5 black balls, and Bag 2 contains...

Bag 1 contains 4 white balls and 5 black balls, and Bag 2 contains nn white balls and 3 black balls. One ball is drawn randomly from Bag 1 and transferred to Bag 2. A ball is then drawn randomly from Bag 2. If the probability, that the ball drawn is white, is 29/4529 / 45, then nn is equal to :

Options

  1. A6
  2. B3
  3. C5
  4. D4

Correct answer

A. 6

Step-by-step solution

Bag 1→4w,5B1 \rightarrow 4 w, 5 B Bag 2→nw,3B(2 \rightarrow n w, 3 B (\mathrm{I})→) \rightarrow Transferred ball is white P(w)=n+1n+4⋅49P(w)=\frac{n+1}{n+4} \cdot \frac{4}{9} (II) \rightarrowTransferredballisblackTransferred ball is blackP(w)=59\frac{5}{9} \cdot nn+4\frac{n}{n+4} 4n+49n+36+5n9n+36=29459n+49n+36=2945⇒n=6\begin{aligned} & \frac{4 n+4}{9 n+36}+\frac{5 n}{9 n+36}=\frac{29}{45} \\ & \frac{9 n+4}{9 n+36}=\frac{29}{45} \Rightarrow n=6 \end{aligned}
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