- 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**

Suppose you are modeling long-term interest rates, and you believe that the supply of corporate debt is a major contributing factor. Suppose you believe that the probability that rates will rise if the supply of corporate debt rises is 60%. If the supply of corporate debt stays constant, you believe that there is a 35% chance of increasing interest rates. If the supply of corporate debt falls, you believe that there is a 5% chance of rates increasing. You think that the likelihood of corporate debt increasing is 50%, staying the same is 40%, and dropping is 10%. What is the unconditional probability of interest rates rising?

B. 55.4%

C. 55.5%

A. 44.5%

B. 55.4%

C. 55.5%

Correct Answer: A

We use the total probability rule: P(A), the unconditional probability, = P(A|S_1)*P(S_1) + P(A|S_2) *P(S_3) + P(A|S_3) *P(S_3), where the S_i represents mutually exclusive and exhaustive events. The likelihood of interest rates increasing is 0.60 * 0.50 + 0.35 * 0.40 + 0.05 * 0.10 = 0.30 + 0.14 + 0.005 = 0.445.

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**User Contributed Comments**
8

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

chek |
can any one explain plz... |

eb2568 |
chek, the problem is simply asking you to find the expected value given the mentioned scenarios. to find an accurate value you must take each scenarios return multiplied by its probability of happening...i.e. .5x.6 + .35x.4 + .1x.05 equals .445 or 44.5% |

Rotigga |
A=rates rise B1=corporate debt rises; B2=corporate debt stays same; B3=corporate debt falls P(A|B1)=0.6 P(A|B2)=0.35 P(A|B3)=0.05 P(B1)=0.5; P(B2)=0.4; P(B3)=0.1 P(A) = 0.6*0.5 + 0.35*0.4 + 0.05*0.1 = 0.445 |

StanleyMo |
thanks Rotigga |

Beret |
Just draw a tree diagram. Then it is easy to see. |

Safiya921 |
The figure given by the answer gives us the Conditional Probability of Interest Rates rising. The unconditional probability is 1-Conditional Probability, so it should be 55.5% |

dada |
That is the unconditional probability, @Safiya921. Check the textbook definition. |

khalifa92 |
this is exactly the same as finding the weighted average. |