- 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 probability that events A and B do not occur simultaneously equals 0.77. The probability of neither A nor B occurring equals 0.38. If P(A) equals 0.26, the probability of B occurring equals ______.

A. 0.43

B. 0.59

C. 0.62

**Explanation:**The probability that events A and B occur simultaneously equals one minus the probability that events A and B do not occur simultaneously. Thus, P(A and B) = 1 - 0.77 = 0.23.

The probability of either A or B occurring equals one minus the probability of neither A nor B occurring. Thus, P(A or B) = 1 - 0.38 = 0.62.

Now, P(A or B) = P(A) + P(B) - P(A and B). Therefore, P(B) = P(A or B) - P(A) + P(A and B) = 0.62 - 0.26 + 0.23 = 0.59.

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**User Contributed Comments**
5

User |
Comment |
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Xocrevilo |
The algebra simple. Just remember that all you really need to know for Level 1 Probability questions is: P(AB) = P(B|A) * P(A) , which is known as the joint probability function, and P(A or B) = P(A) + P(B) - P(A and B). |

Yurik74 |
Great question!!! |

Allen88 |
Good question |

mali97 |
lmfao |

izzarivera |
does anyone know how to input this on BA Plus? |