25 % of the population are smokers. A smoker has 27 times more chances to develop lung cancer then a non-smoker. A person is diagnosed with lung cancer and the probability that this person is a smoker is k 10 .Then the value of k is _____ .

Step-by-step solution

Given, In a city, 25 % of the population is smoker So, P smoker = 0 . 25 P non-smoking = 0 . 75 And smoker has 27 times more chance of being diagnosed with lung cancer, So, if P Lung cancer non-smoker = p then P Lung cancer smoker = 27 p , Now, a person is selected at random and found to be diagnosed with lung cancer, So, total probability of having a lung cancer will be P Lung cancer = 0 . 25 × 27 p + 0 . 75 × p So the probability of him being smoker (using bayes' theorem) will be P sm