One of the two boxes, box I and box II, was selected at random and a ball was drawn randomly out of this box.

Question

Let n₁ and n₂ be the number of red and black balls, respectively, in box I. Let n₃ and n₄ 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 ball 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 values of n₁, n₂, n₃ and n₄ is(are) 

(A) n₁ = 3, n₂ = 3, n₃ = 5, n₄ = 15 

(B) n₁ = 3, n₂ = 6, n₃ = 10, n₄ = 50 

(C) n₁ = 8, n₂ = 6, n₃ = 5, n₄ = 20 

(D) n₁ = 6, n₂ = 12, n₃ = 5, n₄ = 20

Answer 1

Answer is (A), (B)

See Fig.

which are satisfied by options (A) and (B).