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. One of the two boxes, box I and box II, was selected at random and a ball was d

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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. One of the two boxes, box I and box II, was selected at random and a ball was drawn randomly out of this box. The balls was found to be red. If the probability that this red ball was drawn from box II is 1 3 , then the correct option(s) with the possible valu

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Correct answer: A. n 1 = 3 , n 2 = 3 , n 3 = 5 , n 4 = 15

1 3 = 1 2 n 3 n 3 + n 4 1 2 n 1 n 1 + n 2 + n 3 n 3 + n 4 1 3 = n 3 n 3 + n 4 n 1 n 1 + n 2 + n 3 n 3 + n 4 (i) R H S 5 20 5 20 + 3 6 = 1 4 1 4 + 1 2 = 1 4 1 + 2 4 = 1 3 (ii) R H S 10 60 10 60 + 3 9 = 1 6 1 6 + 1 3 = 1 6 1 2 = 1 3 (iii) 5 25 8 14 + 5 25 = 1 5 4 7 + 1 5 = 1 5 20 + 7 35 = 7 27 (iv) 5 25 6 18 + 5 25 = 1 5 5 + 3 15 = 1 5 8 15 = 1 5 × 15 8 = 3 8 .

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