- CFA Exams
- CFA Level I Exam
- Topic 1. Quantitative Methods
- Learning Module 4. Common Probability Distributions
- Subject 5. Binomial Distribution
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.
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 |