- CFA Exams
- CFA Level I Exam
- Topic 1. Quantitative Methods
- Learning Module 4. Probability Trees and Conditional Expectations
- Subject 3. Bayes' Formula and Updating Probability Estimates

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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?

B. 0.429

C. 0.571

A. 0.280

B. 0.429

C. 0.571

Correct Answer: C

Let A

_{1}denote the event that a randomly selected voter is male, A_{2}denote a female, and B denote the event that a randomly selected voter is a Democrat. Using Bayes' rule: P(A_{2}|B) = [P(B|A_{2}) x P(A_{2})]/[P(B|A_{1}) x P(A_{1}) + P(B|A_{2}) x P(A_{2})] = 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 :) |