- CFA Exams
- CFA Level I Exam
- Study Session 2. Quantitative Methods (1)
- Reading 8. 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 student's grade in a course is determined by her score on two exams. The probability that she passes the first exam is 0.85, the probability that she passes the second exam is 0.80, and the probability that she passes both exams is 0.78. What is the probability that she passes at least one of the exams?

A. 0.05

B. 0.83

C. 0.87

**Explanation:**Let A denote the event that she passes the first exam and B denote the event that she passes the second exam. P(A or B) = P(A) + P(B) - P(A and B) = 0.85 + 0.80 - 0.78 = 0.87

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**User Contributed Comments**
2

User |
Comment |
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1a2a |
This is only true if the two events are independent, which is never specified in the problem? |

myexam |
No, @1a2a: it does not matter if they are independent or not. If they are, P(A and B) = 0. In fact, because P(A and B) = 0.78 they are not independent. |