1. The problem statement, all variables and given/known data In a certain club, one-fifth of its members are smokers. One-sixth of its male members are smokers. Among the non-smoking members, one-eighth are female. A member is randomly chosen. (a) What is the probability that this member is male; (b) If this member is female, what is the probability that she is a non-smoking member. (Answers: (a) 21/25 (b) 5/8) 2. Relevant equations Probability Formulae 3. The attempt at a solution One of my friends told me the followings in order to get the final answer correct. However, I don't know how can he get them. (a) (1 - 1/5) * (1 - 1/8) / (1 - 1/6) = 7/10 / (5/6) = 21/25 (b) (1 - 1/5) * 1/8 / (1 - 21/25) = 1/10 / (4/25) = 1/10 * 25/4 = 5/8 I tried to write a tree diagram as follows: S = 1/5 NS = 4/5 S.M = 1/6 S.F = 5/6 NS.M = 7/8 NS.F = 1/8 S: Smoker; NS: Non-Smoker; M: Male; F: Female Did my tree diagram correct? My attempt on part (a): P(M) = P(M|S)P(S) + P(M|NS)P(NS) = 1/6 * 1/5 + 7/8 * 4/5 = 11/15 My attempt on part (b): P(NS|F) = P(NS and F) / (P(F|S)P(S) + P(F|NS)P(NS)) = 4/5 * 1/8 / (1/5 * 5/6 + 4/5 * 1/8) = 3/8 But my answers are not correct. Can anyone tell me how to solve this question? Thank you very much!