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 B

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, is 29/45 , then n is equal to :

TestHub · Accepted Answer

Bag 1 → 4 w , 5 B Bag 2 → n w , 3 B ( I ) → Transferred ball is white P ( w ) = n + 4 n + 1 ​ ⋅ 9 4 ​ (II) → Transferred ball is black P ( w ) = 9 5 ​ ⋅ n + 4 n ​ ​ 9 n + 36 4 n + 4 ​ + 9 n + 36 5 n ​ = 45 29 ​ 9 n + 36 9 n + 4 ​ = 45 29 ​ ⇒ n = 6 ​

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