Of all smokers in particular district, 40% prefer brand A and 60% prefer brand B. Of those who prefer brand A, 30% are female, and of those who prefer brand B, 40% are female.
Q: What is the probability that a randomly selected smoker prefers brand A, given that the person selected is a female?
P(F) = P(F|A)*P(A) + P(F|B)*P(B)
P(F) = 0.3*0.4 + 0.4*0.6 = 0.36
So, 36% of all the smokers are female.
You are looking for P(A|F)
P(A|F) = P(A and F)/P(F)
P(A|F) = (P(F|A)*P(A))/P(F)
P(A|F) = (0.3 * 0.4)/0.36
P(A|F) = 0.33 or 33%
Q: What is the probability that a randomly selected smoker prefers brand A, given that the person selected is a female?
P(F) = P(F|A)*P(A) + P(F|B)*P(B)
P(F) = 0.3*0.4 + 0.4*0.6 = 0.36
So, 36% of all the smokers are female.
You are looking for P(A|F)
P(A|F) = P(A and F)/P(F)
P(A|F) = (P(F|A)*P(A))/P(F)
P(A|F) = (0.3 * 0.4)/0.36
P(A|F) = 0.33 or 33%