- CFA Exams
- CFA Level I Exam
- Topic 1. Quantitative Methods
- Learning Module 3. Probability Concepts
- Subject 9. Bayes' Formula

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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?

B. 0.0340

C. 0.5455

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(A

_{2}| B) = [P(B|A_{2}) x P(A_{2})] / [P(B|A_{1}) x P(A_{1}) + P(B|A_{2}) x P(A_{2}) + P(B|A_{3}) x P(A_{3})] = 0.012 / 0.022 = 0.5455.###
**User Contributed Comments**
9

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?? |

Seancfa1 |
Read the manual! 2nd format choose amount of d.p enter 2nd quit |

thebkr7 |
@Harpalani. Perfectly explained Thanks |

cfastudypl |
Well done Harpalani, I agree with you, because following the basic way of computing for probability will yield the same result. |