Question

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. $\frac{7}{45}$
• B. $\frac{8}{45}$
• C. $\frac{14}{45}$
• D. $\frac{28}{45}$

Answer 1

The correct option is D $\frac{28}{45}$

Based on Bayes' theorem,
Required Probability
$=\frac{(\frac{160}{400}\times \frac{35}{100})}{(\frac{160}{400}\times \frac{35}{100})+(\frac{100}{400}\times \frac{20}{100})+(\frac{140}{400}\times \frac{10}{100})}$
$=\frac{5600}{9000}$
$=\frac{28}{45}$