- 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**

Suppose that stocks A, B, C, and D are independent with respect to their price movement and have probabilities of increasing of 0.25, 0.50, 0.40, and 0.30. What is the probability that stocks A and C will increase in price while stocks B and D will fail to increase?

A. 10%

B. 2.5%

C. 3.5%

**Explanation:**If these events are independent, the joint probability of them occurring together is just the product of the individual probabilities. So, P(AC) = 0.25 * 0.40 = 10%. To this, we multiply the probabilities of B and D failing to increase: 10% * (1 - 0.50)*(1 - 0.30) = 3.5%.

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**User Contributed Comments**
4

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

mtcfa |
PLease help explain this problem; I am confused. |

mtcfa |
All the events are independent, so the calculation is thus: For A and C it is simply .25 x .4 = .1. For B and D you have to multilply .5 x .7 (the probabilities that each will DECREASE) = .35. Then multiply .1 x .35 = .035. |

dimos |
Independent events. So: 0.25 * (1 - 0.5) * 0.4 * (1 - 0.3) = 3.5% |

azramirza |
0.25*0.50(1-.50)*0.40*0.70(1-.30)=0.0350 |