- CFA Exams
- CFA Level I Exam
- Topic 1. Quantitative Methods
- Learning Module 4. Probability Trees and Conditional Expectations
- Subject 2. Probability Trees and Conditional Expectations

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**CFA Practice Question**

A box of candy contains three types of candy: dark chocolate (DC), white chocolate (WC), and peanut butter (PB). There are 24 pieces of candy in the box, 8 of each kind. All pieces are wrapped in the same material and there is no way of finding out what kind of candy one has until one unwraps the candy. An experiment consists of selecting pieces of candy randomly and identifying each piece. Once a piece of candy has been removed from the box, it is not put back in the box. Consider the following events: A, observing a chocolate piece, A=(WC,DC), and B, selecting four pieces of candy such that B=(PB,DC).

Which of the following statements is correct?

A. Events A and B are not mutually exclusive.

B. Events A and B are not exhaustive.

C. Events A and B may or may not be in the same sample space.

**Explanation:**Events A and B are not mutually exclusive. The two events are not mutually exclusive nor disjoint because they share common outcomes. The events A and B are exhaustive because they cover all possible outcomes. A and B are a subset of the same sample space.

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**User Contributed Comments**
5

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

surob |
Still unclear for me. Can someone clarify |

bobert |
Mutually exclusive means that the 2 events cannot happen at the same time, however, DC is part of both events. So being chocolate or one of the selected candies it would encompass both events making the events not mutually exclusive. |

romankuzyk |
How are these events exhaustive though? |

HALIRU79 |
I am with romankuzyk on this: how is this experiment exhaustive. |

dbalakos |
An experiment is exhaustive when an event includes all possible outcomes, here the three types of candy. |