Verified Solution • 2025–26 Session moderate

QJEEM25Ma318d: JEE Main 2025 Mathematics - Class 12 JEEM25Ma318d Solution: Bag 1 contains 4 white balls and 5 black balls, and Bag 2…

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 2945\frac{29}{45} , then n is equal to:

Multiple Choice Options

  • A 5
  • B 6
  • C 4
  • D 3

Step-by-Step Verified Solution

amp; Bag 1={4 W,5 B}amp; Bag 2={nW,3B}amp;P( WBag2)=2945amp;⇒P( W B1)×P( W B2)+P( B B1)×P( W B2)=2945amp;49×n+1n+4+59×nn+4=2945\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}

n=6\mathrm{n = 6}

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