- CFA Exams
- CFA Level I Exam
- Topic 1. Quantitative Methods
- Learning Module 3. Probability Concepts
- Subject 4. Multiplication Rule for Independent Events

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**CFA Practice Question**

An automatic machine inserts mixed vegetables into a plastic bag. Past experience revealed that some packages were underweight and some were overweight, but most had satisfactory weight.

Underweight 2.5

Satisfactory 90.0

Overweight 7.5

Weight % of Total

Underweight 2.5

Satisfactory 90.0

Overweight 7.5

Three packages are selected from the food processing line. What is the probability of selecting and finding that all three of them are underweight?

A. 0.0000156

B. 0.075

C. 0.0000001

**Explanation:**P(all three underweight) = 0.025*0.025*0.025 = 0.0000156

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**User Contributed Comments**
5

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

chamad |
we have to be careful with calculator. Mine ave me 0 because setteled on 4 decimals |

naomixs |
If you press 2nd Format on your BAII calculator you can increase the number of decimal places. |

dash1s |
Why are these probabilities independent? |

farhan92 |
well the probabilities are from past experience so wouldn't be adjusted. |

nmech1984 |
Are independent because it says "from the processing line". So when you pick one, the sample is again the same size. |