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 :

Step-by-step 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 P A = 160 400 P B = 100 400 P C = 140 400 P E A = 35 100 P E B = 20 100 P E C = 10 100 To find P A E = P A P E A P A · P E A + P B · P E B + P C · P E C = 160 400 × 35 100 160 400 × 35 100 + 100 400 × 20 100 + 140 400 × 10 100 = 28 45 option 4