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

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**CFA Practice Question**

Suppose the probability that oil prices will rise during any given quarter is 0.51 and the probability that oil prices will stay level or decline is 0.49. If oil prices rise, GNP will contract by 1% with 80% probability and expand by 0.5% with 20% probability. If oil prices decline or stay level, GNP will expand 3% with a 75% probability and contract 0.5% with a 25% probability. What is the expected change in GNP in the next quarter?

A. -0.86%

B. +0.86%

C. +0.68%

**Explanation:**We use the total probability rule for expected value, for which the formula is E(X) = E(X | S_1) * P(S_1) + E(X |S_2) * P(S_2) + ... + E(X |S_n) * P(S_n). Here, E(X) is the expected change in GNP. S_1 is the event that oil prices rise, and S_2 is the event that oil prices fall. Therefore, E(X) = 0.51 * (-1%*80% + 0.5%*20%) + 0.49 * (3%*75% - 0.5%*25%) = 0.68% (an expansion).

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**User Contributed Comments**
4

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

Pooh |
Note the direction of the oil price (e.g. rise or fall) in the equation. |

chamad |
You're right Pooh...I've missed the answer because of the sign(-)! |

NickPash |
Pooh, it is not the oil price it is the GNP's impact. Contracts (-1) and expands (+3). |

Rsanches |
This question took too many time... |