In a group of $400$ people, $160$ are smokers and non-vegetarian; $100$ are smokers and vegetarian and the remaining $140$ are non-smokers and vegetarian. Their chances of getting a particular chest disorder are $35\%,20\%$ and $10\%$ respectively. A person is chosen from the group at random and is found to be suffering from the chest disorder. The probability that the selected person is a smoker and non-vegetarian is :

• A

  $\frac{14}{45}$
• B

  $\frac{7}{45}$
• C

  $\frac{8}{45}$
• Correct answer
  D

  $\frac{28}{45}$

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