- CFA Exams
- CFA Level I Exam
- Topic 1. Quantitative Methods
- Learning Module 3. Probability Concepts
- Subject 3. Addition Rule for Probabilities: the Probability that at Least One of Two Events Will Occur

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**CFA Practice Question**

A new and relatively obscure pharmaceutical company Nucomp is competing for two large government contracts to produce vaccines for two different diseases. The probability that the company is awarded the first contract is 0.85, the probability that it is awarded the second contract is 0.80, and the probability that it is awarded both contracts is 0.78. What is the probability that Nucomp is awarded at least one of the contracts?

B. 0.87

C. 1.65

A. 0.82

B. 0.87

C. 1.65

Correct Answer: B

Let A denote the event that Nucomp is awarded the first contract and B denote the event that Nucomp is awarded the second contract. P(A or B) = P(A) + P(B) - P(AB) = 0.85 + 0.80 - 0.78 = 0.87

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**User Contributed Comments**
4

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

jpducros |
note that you can eliminate answer c without starting any calculation. |

yesandy11 |
And A as well. |

gill15 |
I'm from the future compared to when you wrote the CFA. 1.65 is a real probability now. |

lhp112 |
We can explain: P(at least one of the contrasts) = 1 - P( No contract) = 1 - [1 - P(A or B)] = P(A or B) |