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Let \( \mathrm{n}_{1} \) and \( \mathrm{n}_{2} \) be the number of red and black balls respectively, in box I. Let \( \mathrm{n}_{3} \) and \( \mathrm{n}_{4} \) be the number of red and black balls, respectively, in box II.
\( \mathrm{P} \)
One of the two boxes, box I and box II, was selected at random and a ball was drawn randomly
W out of this box. The ball was found to be red. If the probability that this red ball was drawn from box II is \( \frac{1}{3} \), then the correct option(s) with the possible values of \( \mathrm{n}_{1}, \mathrm{n}_{2}, \mathrm{n}_{3} \) and \( \mathrm{n}_{4} \) is(are)
(A) \( \mathrm{n}_{1}=3, \mathrm{n}_{2}=3, \mathrm{n}_{3}=5, \mathrm{n}_{4}=15 \)
(B) \( \mathrm{n}_{1}=3, \mathrm{n}_{2}=6, \mathrm{n}_{3}=10, \mathrm{n}_{4}=50 \)
(C) \( \mathrm{n}_{1}=8, \mathrm{n}_{2}=6, \mathrm{n}_{3}=5, \mathrm{n}_{4}=20 \)
(D) \( \mathrm{n}_{1}=6, \mathrm{n}_{2}=12, \mathrm{n}_{3}=5, \mathrm{n}_{4}=20 \)
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