- 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**

Decide if the following events are mutually exclusive and whether or not they are independent or dependent.

Event B: drawing a heart or diamond from a standard deck of 52 cards

B. mutually exclusive, independent

C. mutually exclusive, dependent

Event A: drawing a queen from a standard deck of 52 cards

Event B: drawing a heart or diamond from a standard deck of 52 cards

A. not mutually exclusive, independent

B. mutually exclusive, independent

C. mutually exclusive, dependent

Correct Answer: A

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**User Contributed Comments**
11

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

Cooltallgal |
Can someone please give more explaination on this ? Drawing a queen of heart or diamond will affect both events. |

gnja |
you can draw a queen and a heart or a diamond at the same time (ie by drawing a queen of hearts or diamond)so they're not mutually exclusive (one or the other); but doing so wouldnt affect your chances of drawing a heart or a diamond. |

zilos |
Look at each scenario indepedently |

IIkDII |
k can someone explain this again ... How does drawing a queen of hearts not affect the outcome of either. Event A: you can draw a heart or a diamond (queen) Event B: you can draw a queen (of hearts or diamonds). even if you look at the events independently, these events are not independent. I believe the answer should've been C. |

bobert |
We all know P(A|B) = P(A) for an independent event, right? Or the other way around such that P(B|A) = P(B). Look at each of the events in this manner now to determine whether or not they are independent or dependent. Also note that since we are choosing only 1 card, we do not need to worry about removing cards from the deck so do not over think this one. As discussed before, the events are NOT mutually exclusive. Thank you gnja for that explanation (See above). To further explain the independent or dependent nature of this situation, as I mentioned before, only 1 card is being removed. Therefore there is no reason that picking a single card would be dependent on any other factor as long as the deck is a full deck. Also look for sequence of events when determining dependence. If there was an event prior to picking the 1st card there could be a dependence in this case as there are no less cards. This is usually denoted by the words "given" or "if" in a question. Example: Event A: You flip a coin and it lands heads. Event B: You flip a coin and it lands tails. These are mutually exclusive because you cannot do both at the same time, however they are still independent because Event A does not depend on Event B taking place. The coin is the easiest example to understand, just try to elaborate on and use its context when solving questions like this. Hope that helps. |

sergashev |
thank you bobert |

chamad |
if drawing with replacement A is correct. If with no replacement than the denominator of P(B) will be 51 instead of 52 hence B dependant on A! In this latter case C will be correct answer. Do we have to assume that there is replacement? |

mordja |
Thanks bobert. I was assuming there was no replacement. In reality the question could be making an assessment of the same card, this or replacement would lead to A. |

cleopatraliao |
Thanks gnja for the excellent&brief explaination:D |

denisw123 |
The question doesn't fully specify what's being drawn. Is it: (a) one card only (b) two cards with replacement (c) two cards without replacement We need to know which. |

khalifa92 |
the two outcomes arent mutually exclusive because from two different events, but they would be mutually exclusive in one event. |