JEE MAIN - Mathematics (2023 - 25th January Evening Shift - No. 18)
25% of the population are smokers. A smoker has 27 times more chances to develop lung cancer than a non smoker. A person is diagnosed with lung cancer and the probability that this person is a smoker is $$\frac{k}{10}%$$. Then the value of k is __________.
Answer
9
Explanation
Probability of a person being smoker $=\frac{1}{4}$
Probability of a person being non-smoker $=\frac{3}{4}$
$P\left(\frac{\text { Person is smoker }}{\text { Person diagonsed with cancer }}\right)=\frac{\frac{1}{4} \cdot 27 P}{\frac{1}{4} \cdot 27 P+\frac{3 P}{4}}$
$=\frac{9}{10}=\frac{k}{10}$
$\Rightarrow k=9$
Probability of a person being non-smoker $=\frac{3}{4}$
$P\left(\frac{\text { Person is smoker }}{\text { Person diagonsed with cancer }}\right)=\frac{\frac{1}{4} \cdot 27 P}{\frac{1}{4} \cdot 27 P+\frac{3 P}{4}}$
$=\frac{9}{10}=\frac{k}{10}$
$\Rightarrow k=9$
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