CFA Practice Question

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CFA Practice Question

In Phelps County, the population of registered voters is 60% male and 40% female. Of the males, 20% are Democrats and of the females, 40% are Democrats. If a voter is selected at random and found to be a Democrat, what is the probability that the voter is female?

A. 0.280
B. 0.429
C. 0.571
Correct Answer: C

Let A1 denote the event that a randomly selected voter is male, A2 denote a female, and B denote the event that a randomly selected voter is a Democrat. Using Bayes' rule: P(A2|B) = [P(B|A2) x P(A2)]/[P(B|A1) x P(A1) + P(B|A2) x P(A2)] = 0.16/0.28 = 0.571

User Contributed Comments 15

User Comment
marinachow Can anyone explain this please
ambar We need to know P(F/D)
Given, P(F) = 40%; P(D/F) = 40%
With total Probability Theory,
P(D) = .28
According to Bayes' formula,
P(F/D) = P(D/F)*P(F)/(P(D) = .4*.4/.28 = .571
Beret Once more. Forget about all the formulas like Bayes etc. Just draw a tree diagram to solve all these kind of problems. It works!
panvino Thanks Beret - just tried it and I now understand!!! I also recommend drawing a tree diagram. All those B/As are bound to be cause of error on the day of the exam.
vinooka Thanks Beret! I tried it too...and it's so simple and intuitive.
Jurrens marinachow: to help you clarify a little more: the .28 comes from (.4*.4)+(.6*.2)
EminYus tree diagram = golden!
NikolaZ Once again: Assume 100 voters

60 male (20% democrat) = 12 Male Democrats
40 female (40% democrat) = 16 Female Democrats
=> 28 Democrats in total

P(F|D) = P(FD)/P(D) = 16/28 = 0.57143
johntan1979 If you guys don't get Bayes, then that's sad, because that's the whole point about this section... to understand and apply Bayes, not to test your ability to draw tree diagrams.
Shaan23 Johntan is correct.
schweitzdm Feel free to draw diagrams during the test if it helps you reach the right answer in under 1.5 minutes.
birdperson tree diagram is a way easier way to solve bayes problems
cschulz316 I'm on the tree train too. I watched Brian Veitch's youtube video about using trees with Bayes and it really helps you visualize what the equation means.
zackrivers @johntan1979 if Baye were here, he would compute the success getting the answer right given tree diagram vs answer right given not tree diagram and he would see that that was a stupid calculation to try to figure out, then he would do a long sigh and say "just do the tree diagram".
maryprz14 I LOVE this Bayes guy so much! I hope we get many questions from this topic :)
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