JEE Main · 2025 · 29 Jan 2025 · Shift 2 · Probability

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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:

(A)3
(B)4
(C)5
(D)6✓ Correct

Answer: (D)

Solution

Bag 1:

4

5

B; Bag 2:

n

3

B. Transferring a ball from Bag 1 changes Bag 2 to

(n + 1)

3

B if white was transferred, or

n

4

B if black was transferred.

P (white) = \frac{4}{9} \cdot \frac{n + 1}{n + 4} + \frac{5}{9} \cdot \frac{n}{n + 4} = \frac{9 n + 4}{9 ( n + 4 )}

Setting this to

\frac{29}{45}

45 (9 n + 4) = 29 \cdot 9 (n + 4) \Rightarrow 405 n + 180 = 261 n + 1044 \Rightarrow 144 n = 864 \Rightarrow n = 6

JEE Main · 2025 · 29 Jan 2025 · Shift 2 · Single correct option

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