JEE PYQ: Probability Question 11
Question 11 - 2021 (25 Feb Shift 2)
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:
(1) $\frac{7}{45}$
(2) $\frac{8}{45}$
(3) $\frac{14}{45}$
(4) $\frac{28}{45}$
Show Answer
Answer: (4)
Solution
By Bayes’ theorem: $P = \frac{160 \times \frac{35}{100}}{160 \times \frac{35}{100} + 100 \times \frac{20}{100} + 140 \times \frac{10}{100}} = \frac{5600}{5600 + 2000 + 1400} = \frac{5600}{9000} = \frac{28}{45}$.
BETA
