- 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**

A jar contains 3 red and 5 yellow balls; two balls are randomly selected from the jar. Which of the following is true?

B. The events first pick and second pick are independent events.

C. P(red ball and yellow ball) = 0

D. The events first pick and second pick are dependent events.

A. This is a binomial situation.

B. The events first pick and second pick are independent events.

C. P(red ball and yellow ball) = 0

D. The events first pick and second pick are dependent events.

Correct Answer: D

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**User Contributed Comments**
11

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

surob |
Why? |

Mattik |
Because on pick 1: P(red) = 3/8 and P(yellow) = 5/8 Now, if on pick one you get red, then On pick 2: P(red) = 2/7 and P(yellow) = 5/7 therefore, Pick 1 "affected" pick 2 and they are dependent. If, on the otherhand, the ball chosen on pick 1 were replaced, then pick 1 and pick 2 would be independent (because picking either color on pick 1, would NOT change the P's on pick 2) |

coolnan |
Thanks-Mattik. |

Mikael |
I could not understand why A was not correct. I think this is because the two trials are not independent. So, p cannot be constant (as required by the binomial distribution). |

NikolaZ |
How are these dependent events, and on the previous question when drawing a Queen and then a heart/diamond are independent events? |

Seancfa1 |
NikolaZ, because in this situation you have 2 occurrences of the event, whereas in the Queen vs Heart/Diamond you had only 1 occurrence. If there were multiple occurrences of the Queen vs Heart/Diamond situation it would be a dependent series of probabilities. |

Shaan23 |
Mikael - I dont understand why this is not binomial either. If you were to ask me what is the probility of getting 2 R's I would do 8C2 with p=3/8....a binomial distribution quesiton |

Shaan23 |
Nevermind....Mikael you answered your own question and mine |

garsila |
Can someone explain why the two balls are NOT picked at the same time but in two separate events? There is no indication in the wording of the problem ... can someone please explain! |

garsila |
Why the two balls are NOT picked in the same event? |

gyee2012 |
The assumption. Will there be replacement or without. Without replacement - Picking a ball would be a dependent event rather than independent |