- 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**

Three pharmaceutical companies have contracted with the government for the delivery of three different types of vaccines by January 1, 2012. Because of other work commitments and procedural problems with the FDA, contracting firms cannot always meet the agreed delivery date. The probability that the first vaccine will be delivered on time is 0.7. The probability that the second vaccine will be delivered on time is 0.6, and the probability that third vaccine will be delivered on time is 0.8. If the deliveries are independent of one another, find the probability that all three pharmaceutical companies will meet their deadlines.

B. 0.336

C. 0.980

A. 0.144

B. 0.336

C. 0.980

Correct Answer: B

Let A denote the event that the first vaccine is on time, B denote the event that the second vaccine is on time and C denote the event that the third vaccine is on time. Since the deliveries are independent, the joint probability is P(ABC) = P(A)P(B)P(C) = (0.7)(0.6)(0.8) = 0.336.

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**User Contributed Comments**
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ibrahim18 |
Too much stories for a simple answe |

gyee2012 |
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