- 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**

Students at University X must be in one of the class ranks: freshman, sophomore, junior, or senior. At University X, 35% of the students are freshman and 30% are sophomores. If a student is selected at random, the probability that he or she is either a junior or a senior is ______.

B. 65%

C. 30%

A. 35%

B. 65%

C. 30%

Correct Answer: A

The probability of the event junior or senior is 1 minus the probability that this event does not occur, namely 1 minus the probability of the event freshman or sophomore. Its probability is thus 1 - 0.65 = 0.35.

Using the addition rule, because freshman and sophomore are disjoint, P(freshmen or sophomore) = P(freshman) + P(sophomore) = 0.35 + 0.3 = 0.65.

The probability of the event junior or senior is 1 minus the probability that this event does not occur, namely 1 minus the probability of the event freshman or sophomore. Its probability is thus 1 - 0.65 = 0.35.

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**User Contributed Comments**
3

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

nichmax |
Tricky Qs |

bidisha |
when its "mutually exclusive", if one happens then other cannot happen then don't subtract P(A.B) |

sgossett86 |
i got one right |