Let n _ 1 and n _ 2 be the number of red and black balls,...

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.
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 $\dfrac{1}{3}$ , then the correct options(s) with the possible values of ${n}_{1}and{n}_{2}$ is(are)