### CFA Practice Question

There are 410 practice questions for this study session.

### 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

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 Comment
azramirza Or
.05*.10=0.0050
.03*0.40=0.0120
.01*.50=0.0150
total=0.0220

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??