- 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**

For the tree diagram shown with P(A) = 0.3 and P(B) = 0.6, which of the following is false?

B. Events A and B are dependent.

C. P(not B) = 0.4

D. Events A and B are independent.

A. P(not A) = 0.7

B. Events A and B are dependent.

C. P(not B) = 0.4

D. Events A and B are independent.

Correct Answer: D

We know events A and B are NOT independent events because P(B | A) = 2/3 and it was given that P(B) = 0.6. Because P(B | A) is not equal to P(B), the events are dependent.

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**User Contributed Comments**
14

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

vincenthuang |
B is correct |

Pooh |
How would you know p(not b) is 0.4? anyone? |

jminard |
Vincent: B is not correct. It's false. Pooh: it's given that P(B) = 0.4, so P(not B) is 1 - 0.4 = 0.6 |

Yooo |
jminard is incorrect in both instances. A and B are dependent. The outcome of A affects outcome of B. P(B) is not given. It is possible that the P(notB)= 0.4 |

Rotigga |
D is correct. P(A) = 0.3; P(B) = 0.6 . From the diagram, we get P(A and B) = 0.2, which does not equal P(A) * P(B) = 0.18; therefore, the two events are Dependent. |

bobert |
A) True: P(not A) = .7 --> A is given as P(A)=.3 P(AS) + (PAS^c) = 1 Therefore after filling all in, we get .7 B) True: They are dependent because of the reason posted by Yooo and Rotigga C) True: Same reason as in A). Do not be fooled by the .2 which is not P(B) it is the P(B|A). D) False: Due to the opposite of B). |

StanleyMo |
P (B) = 0.4, so P(not B) =0.6 :) |

JKiro |
Pooh: we are given that the P(B) = 0.6; the complement or the P(not B) = 0.4 |

jlevee |
none of this matters. look at the diagram - if they were independent, you'd have the same probability of reaching B regardless of the outcome of event A. But since A can lead to B, they're dependent. |

Vikku |
I think the confusion occured becoz some of us read the question incorrectly..... Note: it asks which of the choices are false. And answer D is correct. |

elmagico10 |
bobert, the probablility P(B/A) it is not 0.2, that´s the probability P(BA). The probability P(B/A) is 2/3. You can see that with P(BA)=P(B/A)xP(A) 0,2=P(B/A)x0,3 then P(B/A)=0,2/03=2/3 |

dbedford |
P(B)=P(B|A)P(A). P(B)=.2 P(A)=.3 P(B|A)=.2/.3 which if they were independent then P(B) = P(B|A) which it doesn't |

dbedford |
Forget my explanation rotigga's is the best I incorrectly said P(B) was .2 |

zeanww |
The question has typo. They should be dependent. |