CFA Practice Question

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CFA Practice Question

In a certain electric motor factory, production lines 1, 2, and 3 produce 10%, 40%, and 50%, respectively, of the total output. Of their respective outputs, 5%, 3%, and 1% are defective. What is the probability that a defective motor came from production line 2?

A. 0.0220
B. 0.0340
C. 0.5455
Correct Answer: C

Using Bayes' rule, the probability that the motor came from line 2, given that it is defective, is P(A2 | B) = [P(B|A2) x P(A2)] / [P(B|A1) x P(A1) + P(B|A2) x P(A2) + P(B|A3) x P(A3)] = 0.012 / 0.022 = 0.5455.

User Contributed Comments 9

User Comment
azramirza Or

Machine2to be defective=0.0120/0.220=0.0545
EminYus How come there is no multiplication of the event in the above example? I got the answer, but don't understand how it relates to Bayes.

P(E | I) = P(I |E) / P(I) x P(E)
EminYus nevermind, broke it all down and figured it out
harpalani Forget what Bayes said. Let's look at it this way:

Prd Line % Prod. % default Prob. of default
1 10% 5% 0.005
2 40% 3% 0.012
3 50% 1% 0.005

Prob. tht defective production came from prod line 2 = 0.012/(0.005+0.012+0.005) = 54.45%
NikolaZ Bayes formula took forever, I assumed 100 motors, out of 100: 2.2 were defective, out of these 2.2, 1.2 of the defects belonged to Production(2)

Therefore: 1.2/2.2 = 0.5455
bidisha How can i change the settings in my ba2 plus professional so that it will go up to 3 decimal places rather than rounding everything down auto to 2 decimal??
Seancfa1 Read the manual!

2nd format
choose amount of d.p
2nd quit
thebkr7 @Harpalani. Perfectly explained
cfastudypl Well done Harpalani, I agree with you, because following the basic way of computing for probability will yield the same result.
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