Bag $\mathrm{I}$ contains $3$ red, $4$ black and $3$ white balls and Bag $\mathrm{II}$ contains $2$ red, $5$ black and $2$ white balls. One ball is transferred from Bag $\mathrm{I}$ to Bag $\mathrm{II}$ and then a ball is draw from Bag $\mathrm{II}$. The ball so drawn is found to be black in colour. Then the probability, that the transferred ball is red, is

• A

  $\frac{4}{9}$
• Correct answer
  B

  $\frac{5}{18}$
• C

  $\frac{1}{6}$
• D

  $\frac{3}{10}$

Hence, the correct answer is option: 'B'.