Let n 1 a n d n 2 be the number of red and black balls, respectively, in box I. Let n 3 a n d n 4 be the number of red and black balls, respectively, in box II. A ball is drawn at random from box I and transferred to box II. If the probabil

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Let n 1 a n d n 2 be the number of red and black balls, respectively, in box I. Let n 3 a n d n 4 be the number of red and black balls, respectively, in box II. A ball is drawn at random from box I and transferred to box II. If the probability of drawing a red ball from box I, after this transfer, is 1 3 , then the correct options(s) with the possible values of n 1 a n d n 2 is(are)

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Correct answer: C. n 1 = 10 a n d n 2 = 20

Probability = n 1 n 1 + n 2 &sdot; n 1 - 1 n 1 + n 2 - 1 + n 2 n 1 + n 2 &sdot; n 1 n 1 + n 2 - 1 = 1 3 ⇒ n 1 n 1 - 1 + n 2 n 1 n 1 + n 2 ( n 1 + n 2 - 1 ) = 1 3 ⇒ n 1 = 10 , n 2 = 20 or n 1 = 3 , n 2 = 6

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