Mathematics · Probability

JEE Main 2025 — 29 January, Evening Shift — Question 57

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 $29 / 45$ , then n is equal to

Answer: D

Bag $1=\{4 \mathrm{~W}, 5 \mathrm{~B}\}$

Bag $2=\{\mathbf{n W}, \mathbf{3 B}\}$

$\mathrm{P}\left(\frac{\mathrm{W}}{\mathrm{Bag} 2}\right)=\frac{29}{45}$

\Rightarrow P\!\left(\frac{W}{B_1}\right)\times P\!\left(\frac{W}{B_2}\right) + P\!\left(\frac{B}{B_1}\right)\times P\!\left(\frac{W}{B_2}\right) = \frac{29}{45}

$\frac{4}{9} \times \frac{n+1}{n+4}+\frac{5}{9} \times \frac{n}{n+4}=\frac{29}{45}$

$\mathrm{n}=6$

Answer key and solution verified before publishing.

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