- 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**

The manager of a pension fund determines that during the past five years 85 percent of the stocks in the portfolio have paid a dividend and 40 percent of the stocks have announced a stock split. If 95 percent of the stocks have paid a dividend and/or announced a stock split, the joint probability of a stock paying a dividend and announcing a stock split is closest to ______.

A. 25%

B. 30%

C. 40%

**Explanation:**The probability that at least one of two events will occur is the sum of the probabilities of the separate events less the joint probability of the two events.

P(A or B) = P(A) + P(B) - P(AB)

95% = 85% + 40% - P(AB); therefore P(AB) = 30%

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**User Contributed Comments**
2

User |
Comment |
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aleakos |
Is this right? It says the probability that a stock has paid a dividend AND/OR paid a stock is 95 percent. Doesn't this mean that the p(a or b)+ p(ab)=95%, or am I being dumb? |

aleakos |
Nevermind I'm being dumb, or is inclusive |