- 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**

Joan has a 60% probability of making a free-throw. If she shoots two free-throws, what is the probability she misses both of them?

B. 16%

C. 60%

A. 48%

B. 16%

C. 60%

Correct Answer: B

Drawing a tree diagram, the event Miss AND Miss is represented by the bottom branch. The probability of traveling this branch is (0.4)(0.4) = 0.16 = 16%. Thus, P(Joan misses both free-throws) = 16%.

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**User Contributed Comments**
6

User |
Comment |
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tenny45 |
or let A = make first B= make second Then P(A and B) = 0.6*0.6 = 0.36 P (A OR B) = 0.6+0.6-0.36 = 0.84 P (NOT A, NOT B) = 1 - 0.84 = 16% Longer but no graphs. |

bobert |
Or you can simply realize the events are independent of each other which translates to P(AA) = P(A) * P(A) or in this case P(not AA) = P(not A) * P(not A)= P(not AA) = (.4)(.4) = .16 Note: I used P(AA) because there is only 1 event, also indicating no dependence. |

Poorvi |
I did it this way. If p(a) is that she makes the freethrow, then p(a) =0.6 P(a compl) = 1-0.6=0.4 To get two p(a compl) twice, 0.4*0.4=0.16 |

AUAU |
y not 1 - 0.60 x 0.60 = 0.64 |

Zawerthal |
AUAU, that would be the probability of making both free throws |

gyee2012 |
^ I like tenny45's logic for an easy check The or statement pf P(A or B) = .84 Therefore the opposite would equal .16 The faster route is to realize this is independent so the calcuations are straight forward and easy. 0.40^2 = 0.16 |