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:
Correct Option: , 4
Based on Baye's theorem
Probability $=\frac{\left(160 \times \frac{35}{100}\right)}{\left(160 \times \frac{25}{100}\right)+\left(100 \times \frac{20}{100}\right)+\left(140 \times \frac{10}{100}\right)}$
$=\frac{5600}{9000}$
$=\frac{28}{45}$
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