- CFA Exams
- CFA Level I Exam
- Topic 1. Quantitative Methods
- Learning Module 3. Probability Concepts
- Subject 5. The Total Probability Rule

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**CFA Practice Question**

A high school teacher has observed that 45% of students who know music have a grade of B or better in math, versus 36% of students who do not know music. If 55% of students in a class know music, what is the probability of a student getting a grade of B or better?

B. 0.38

C. 0.41

A. 0.27

B. 0.38

C. 0.41

Correct Answer: C

Define event A as being the event in which a student gets a B or an A in math. Using the total probability rule, P(A) = 0.45 x 0.55 + 0.36 x (1-0.55) = 0.41.

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**User Contributed Comments**
4

User |
Comment |
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AndyBear |
Please explain. Thanks! |

kmmcclanahan |
If 55% of the class does know music then we can assume that 45% does not know music. Becuase 45% of the kids that do know music are getting a B or higher and 36% who do not know music are also getting a B or higher we can use the complement Total Probability rule: P (Getting a b) = (.55 (Know music))(.45(Know music and getting a B)) + (.45 (Don't know music))(.36(Dont know music and getting a B)) |

kmmcclanahan |
And obviously that comes out to .41 |

dcfa |
P(G>B/Know music)=0.45 P(Dont know music)=0.45 P(know music)=0.55 P(G>B/Dont know music)=0.36 P(G>B)=P(G>B/Know music) P(know music) + P(G>B/dont know music) P(dont know music) = 0.45 * 0.55 + 0.36 * 0.45 = 0.4095 ~ 0.41 |