- CFA Exams
- CFA Level I Exam
- Topic 1. Quantitative Methods
- Learning Module 3. Probability Concepts
- Subject 5. The Total Probability Rule

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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. An electric motor is selected at random. What is the probability that the motor is defective?

B. 0.090

C. 0.978

A. 0.022

B. 0.090

C. 0.978

Correct Answer: A

P(B) = P(B|A

Let A

_{i}denote the event that the motor came from line i, where i = 1, 2, 3, and B denote the event that the motor is defective. Using the total probability rule:P(B) = P(B|A

_{1})P(A_{1}) + P(B|A_{2})P(A_{2}) + P(B|A_{3})P(A_{3}) = 0.05 x 0.10 + 0.03 x 0.40 + 0.01 x 0.50 = 0.022.###
**User Contributed Comments**
3

User |
Comment |
---|---|

Amrokken |
Straighforward 1 |

ANBobby |
Does that add up correctly? |

ANBobby |
oops nevermind |