- CFA Exams
- CFA Exam: Level I 2021
- Study Session 2. Quantitative Methods (1)
- Reading 8. Probability Concepts
- Subject 5. The Total Probability Rule

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**CFA Practice Question**

The organizers of an outdoor event know that the success of the event depends on the weather. It costs $50,000 to stage the event. If the weather is favorable, the organizers will take in $200,000. If the weather is moderate, the organizers will take in $80,000. If the weather is unfavorable, the organizers will be forced to abandon the event, and thus take in $0. The weather bureau forecasts that the chances of favorable, moderate, and unfavorable weather are 20%, 30%, and 50%, respectively.

II. E(X|M) = 80,000

III. E(X|U) = 0

IV. E(X) = 200000*0.2 + 80000*0.3 + 0*0.5 = 64000

Assume: X = revenue, F = favorable weather, M = moderate weather, U = unfavorable weather.

When calculating the expected value:

I. Expected value (Revenue| Favorable weather) = 200,000

II. E(X|M) = 80,000

III. E(X|U) = 0

IV. E(X) = 200000*0.2 + 80000*0.3 + 0*0.5 = 64000

Which statement(s) is (are) TRUE?

Correct Answer: I, II, III and IV

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**User Contributed Comments**
8

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

fmhp |
what about the initial $50000 to stage the event? Should be mentioned that this is included in the money earned or not. |

NikolaZ |
Only IV is correct using the total probability rule. I, II, III are correct using the conditional probability rule. |

leftcoast |
fmhp - X = revenue, as in before any costs are deducted. |

nabilhjeily |
i agree with nicolaz the other are conditional read the question man... |

Amrokken |
is/are true...key words |

choas69 |
whenever the answers are with old greek then its multi right answer |

forry9er |
@choas69 ... no questions on the CFA are presented in the "Old Greek" fashion. Beating the Analystnotes questions isn't the key to preparation. |

khalifa92 |
nicely said |