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,

Question

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, 29/45, then n is equal to : [2025]

Smart Achievers · Accepted Answer

(2)

We have, Bag 1 : {4W, 5B} and Bag 2 : {nW, 3B}

Also, P(W/Bag 2) = $\frac{29}{45}$

$\Rightarrow P (\frac{W}{B_{1}}) \times P (\frac{W}{B_{2}}) + P (\frac{B}{B_{1}}) \times P (\frac{W}{B_{2}}) = \frac{29}{45}$

$\Rightarrow \frac{4}{9} (\frac{n + 1}{n + 4}) + \frac{5}{9} (\frac{n}{n + 4}) = \frac{29}{45} \Rightarrow \frac{4 n + 4 + 5 n}{9 n + 36} = \frac{29}{45}$

$\Rightarrow \frac{9 n + 4}{9 n + 36} = \frac{29}{45} \Rightarrow 405 n + 180 = 261 n + 1044$

$\Rightarrow 144 n = 864 \Rightarrow n = 6$ .

Solution

Q.
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, 29/45, then n is equal to : [2025]

1 4

2 6

3 3

4 5

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Solution

Q. 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, 29/45, then n is equal to : [2025]

1 4

2 6

3 3

4 5

Ans. (2) We have, Bag 1 : {4W, 5B} and Bag 2 : {nW, 3B} Also, P(W/Bag 2) = 2945 ⇒ P(WB1)×P(WB2)+P(BB1)×P(WB2)=2945 ⇒ 49(n+1n+4)+59(nn+4)=2945 ⇒ 4n+4+5n9n+36=2945 ⇒ 9n+49n+36=2945 ⇒ 405n+180=261n+1044 ⇒ 144n=864 ⇒ n=6.

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Q.
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, 29/45, then n is equal to : [2025]