JEE MAIN - Mathematics (2025 - 29th January Evening Shift - No. 9)
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:
5
6
4
3
Explanation
$$\begin{aligned} & \text { Bag } 1=\{4 \mathrm{~W}, 5 \mathrm{~B}\} \\ & \text { Bag } \mathbf{2}=\{\mathbf{n W}, \mathbf{3 B}\} \\ & \mathrm{P}\left(\frac{\mathrm{~W}}{\mathrm{Bag} 2}\right)=\frac{29}{45} \\ & \Rightarrow \mathrm{P}\left(\frac{\mathrm{~W}}{\mathrm{~B}_1}\right) \times \mathrm{P}\left(\frac{\mathrm{~W}}{\mathrm{~B}_2}\right)+\mathrm{P}\left(\frac{\mathrm{~B}}{\mathrm{~B}_1}\right) \times \mathrm{P}\left(\frac{\mathrm{~W}}{\mathrm{~B}_2}\right)=\frac{29}{45} \\ & \frac{4}{9} \times \frac{\mathrm{n}+1}{\mathrm{n}+4}+\frac{5}{9} \times \frac{\mathrm{n}}{\mathrm{n}+4}=\frac{29}{45} \end{aligned}$$
$\mathrm{n = 6}$
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