- CFA Exams
- CFA Exam: Level I 2021
- Study Session 3. Quantitative Methods (2)
- Reading 9. Common Probability Distributions
- Subject 5. The Binomial Distribution

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**CFA Practice Question**

Albert is taking a 10-item multiple-choice test (4 choices per item) and randomly guessing on each item. How many items should he expect to get correct?

B. 3

C. 2

A. 2.5

B. 3

C. 2

Correct Answer: A

This is a binomial situation. The independent trials of the same act guessed at are item-N = 10. Each trial has exactly 2 outcomes (get item correct, get item incorrect); p, the probability of success, is 1/4. So, let random variable x count the number of items Albert gets correct and x be a random variable from a binomial experiment with N = 10 and p = 0.25. The expected value of x (the expected number of correct items) is the mean, m = Np. Here, m = (10)(0.25) = 2.5. So, Albert should expect to get 2.5 items correct.

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**User Contributed Comments**
5

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

srinitest123 |
since the sample size is discrete 1 through 10 though the probalibility is 2.5, number of items need to be either 2 or 3, am i correct? |

bahodir |
Yeah, if he is taking the test once. But taking a test for many times gives a mean of 2.5 |

bobert |
Also, it says how many should he EXPECT. That means that it is not an exact number. Expected values are nothing more than means. |

TammTamm |
I guessed at this one too. 10/4=2.5 Quant is not a strong area for me. |

salmum |
in the same way , the items expected to clear cfa level 1 with random guessing would be - .333*240=79.92 ,, :p |