Let n 1 and n 2 be the number of red and black balls, respectively, in box I . Let n 3 and n 4 be the number of red and black balls, respectively, in box II .
(i) 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 ball was found to be red. If the probability that this red ball was drawn from box II is 
, then the correct option(s) with the possible values of n 1 , n 2 , n 3 and n 4 is(are)
Text Solution
Verified by Experts(i)(a,b); (ii)(c,d)
(i)(a,b)
Sol. 
P(R) = 
R( II /R) = 
= 
by option n 1 = 3, n 2 = 3, n 3 = 5, n 4 = 15
P( II /R) = 
(ii)(c,d)
Sol. Given 
3(n 12 – n 1 + n 1 n 2 ) = (n 1 + n 2 )(n 1 + n 2 – 1)
3n 1 (n 1 + n 2 – 1) = n 1 + n 2 (n 1 + n 2 – 1)
2n 1 = n 2
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