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 (integer)
9
Solution
Probability of a person being smoker $=\frac{1}{4}$
<br/><br/>
Probability of a person being non-smoker $=\frac{3}{4}$
<br/><br/>
$P\left(\frac{\text { Person is smoker }}{\text { Person diagonsed with cancer }}\right)=\frac{\frac{1}{4} \cdot 27 P}{\frac{1}{4} \cdot 27 P+\frac{3 P}{4}}$
<br/><br/>
$=\frac{9}{10}=\frac{k}{10}$
<br/><br/>
$\Rightarrow k=9$
About this question
Subject: Mathematics · Chapter: Probability · Topic: Classical and Axiomatic Probability
This question is part of PrepWiser's free JEE Main question bank. 143 more solved questions on Probability are available — start with the harder ones if your accuracy is >70%.