Paragraph: A box $B_{1}$ contains $1$ white ball, $3$ red balls and $2$ black balls. Another box $B_{2}$ contains $2$ white balls, $3$ red balls and $4$ black balls. A third box $B_{3}$ contains $3$ white balls, $4$ red balls and $5$ black balls.
Question: If $2$ balls are drawn (without replacement) from a randomly selected box and one of the balls is white and the other ball is red, the probability that these $2$ balls are drawn from box $B_{2}$ is

• A

  $\frac{116}{181}$
• B

  $\frac{126}{181}$
• C

  $\frac{65}{181}$
• Correct answer
  D

  $\frac{55}{181}$

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