CFA Practice Question

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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?

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.

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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