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Basic Question 3 of 4
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
User Contributed Comments 4
| User | Comment |
|---|---|
| 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 |
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Learning Outcome Statements
calculate and interpret an unconditional probability using the total probability rule;
CFA® 2024 Level I Curriculum, Volume 1, Module 3.