- #1
chrisyuen
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Homework Statement
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)
Homework Equations
Probability Formulae
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!