- 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**

At a certain university, 42% of the students are women and 18% are engineering majors. Of the engineers, 22% are women. If a student at this university is selected at random, what is the probability that the selected person is a woman or an engineering major?

B. 0.5604

C. 0.6000

A. 0.0396

B. 0.5604

C. 0.6000

Correct Answer: B

Since P(A and B) = P(B) x P(A|B) = 0.18 x 0.22 = 0.0396

P(A or B) = 0.42 + 0.18 - 0.0396 = 0.5604.

Let A be the event that a woman is selected and B be the event that an engineering major is selected. We are given the information that P(A) = 0.42, P(B) = 0.18, and P(A|B) = 0.22. According to the general addition rule, P(A or B) = P(A) + P(B) - P(A and B).

Since P(A and B) = P(B) x P(A|B) = 0.18 x 0.22 = 0.0396

P(A or B) = 0.42 + 0.18 - 0.0396 = 0.5604.

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**User Contributed Comments**
7

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

Gina |
why not simply: P(AorB)= 0.42 + 0.18 - 0.22=0.38 p(women)+p(engineers)-p(women engineers) since women engineers is the overlapping category we have counted twice. ? |

Gina |
ignore the above. obviously it cannot be less than 42%, in the first place. 22% of 18% = 3.96% = p(women engineers) that have been counted twice. |

wundac |
thsnkd gina. I had the same thought |

fedha |
P(W)=0.42 P(E)=0.18 P(W|E)=0.22 P(WorE)=? We know that P(WE)= P(W|E)* P(E) Therefore (0.22*0.18) = 0.0396 We also know P(WorE) = P(W)+P(E)?P(WE) Therefore 0.42 + 0.18 - 0.0396 = 0.5604 |

morek |
Thank you fedha. That is the best way to calculate it. |

jgraham6 |
I was an engineering major in college. Trust me, there were hardly any women in my classes. I should've been a child psychology major. |

2014 |
In that u wud have married womens in ur clinic But withs their kids, and probability of their husbands too. Keyword in this question is women or engineering major in earlier question they refered only to eng women. So clue to remember this question: u never get same women in ur life again. so why to double count them |