Class JEE Mathematics Statistics and Probability Q #989
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4 Marks 2025 JEE Main 2025 (Online) 29th January Evening Shift MCQ SINGLE
Bag 1 contains 4 white balls and 5 black balls, and Bag 2 contains n 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 $\frac{29}{45}$, then n is equal to:
(A) 5
(B) 6
(C) 4
(D) 3
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Correct Answer: B
Explanation
Bag $1 = \{4 W, 5 B\}$
Bag $2 = \{nW, 3B\}$
$P(\frac{W}{Bag2}) = \frac{29}{45}$
$\Rightarrow P(\frac{W}{B_1}) \times P(\frac{W}{B_2}) + P(\frac{B}{B_1}) \times P(\frac{W}{B_2}) = \frac{29}{45}$
$\frac{4}{9} \times \frac{n+1}{n+4} + \frac{5}{9} \times \frac{n}{n+4} = \frac{29}{45}$
$n = 6$

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