In group of 400 people find probability of... | Probability

JEE MAIN 2021

25-02-2021 S2

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 :

Select the correct option:

$\frac{7}{45}$

$\frac{14}{45}$

$\frac{28}{45}$

$\frac{8}{45}$

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution

Consider following events
A : Person chosen is a smoker and non vegetarian.
B : Person chosen is a smoker and vegetarian.
C : Person chosen is a non-smoker and vegetarian.
E : Person chosen has a chest disorder
Given $$ \begin{aligned} & P(A)=\frac{160}{400} P(B)=\frac{100}{400} P(C)=\frac{140}{400} \\ & P\left(\frac{E}{A}\right)=\frac{35}{100} P\left(\frac{E}{B}\right)=\frac{20}{100} P\left(\frac{E}{C}\right)=\frac{10}{100} \end{aligned} $$ To find $$ \begin{aligned} & P\left(\frac{A}{E}\right)=\frac{P(A) P\left(\frac{E}{A}\right)}{P(A) \cdot P\left(\frac{E}{A}\right)+P(B) \cdot P\left(\frac{E}{B}\right)+P(C) \cdot P\left(\frac{E}{C}\right)} \\ & =\frac{\frac{160}{400} \times \frac{35}{100}}{\frac{160}{400} \times \frac{35}{100}+\frac{100}{400} \times \frac{20}{100}+\frac{140}{400} \times \frac{10}{100}} \\
& =\frac{28}{45} \end{aligned} $$

Question Tags

JEE Main

Mathematics

Hard

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