Question

$25 \%$ 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 1

The correct answer is 9.
E1​: Smokers
P(E1​)=41​
E2​: non-smokers
P(E2​)=43​
E : diagnosed with lung cancer
P(E/E1​)=2827​
P(E/E2​)=281​
P(E1​/E)=P(E)P(E1​)P(E/E1​)​
=41​×2827​+43​×281​41​×2827​​=3010​279​=109​
K=9