The sample includes 30% of women and 70% of men. It is known that among them 10% of women and 60% of men smoke. Person X is known to be a non-smoker. Find the probability that X is male.

Question

The sample includes 30% of women and 70% of men. It is known that among them 10% of women and 60% of men smoke. Person X is known to be a non-smoker. Find the probability that X is male.

Answer 1

P(nonsmoker|male) = 1 - P(smoker|male) = 1 - .6 = .4

P(nonsmoker|female) = 1 - P(smoker|female) = 1 - .1 = .9

P(male|nonsmoker) =

P(male and nonsmoker)/P(nonsmoker) =

P(nonsmoker and male)/(P(nonsmoker and male)+P(nonsmoker and female)) =

P(nonsmoker|male)P(male)/(P(nonsmoker|male)P(male)+P(nonsmoker|female)P(female)) =

(.4)(.7)/(((.4)(.7)+(.9)(.3)) =

.28/(.28+.27) =

28/55