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 $\frac{1}{3}$ , then the correct options(s) with the possible values of $n_{1}and n_2$ is(are)

• A

  $n_1=4 and n_2=6$
• B

  $n_1=2 and n_2=3$
• Correct answer
  C

  $n_1=10 and n_2=20$
• Correct answer
  D

  $n_1=3 and n_2=6$

Hence, the correct answer is options: 'C', 'D'.