- CFA Exams
- CFA Level I Exam
- Study Session 3. Quantitative Methods (2)
- Reading 9. Common Probability Distributions
- Subject 5. The Binomial Distribution
CFA Practice Question
Sixty percent of the customers of a fast food chain order the Whopper, fries, and a drink. If a random sample of 15 cash register receipts is selected, what is the probability that 10 or more will show that the above three food items were ordered?
A. 0.403
B. 0.186
C. Neither of these answers
Explanation: This is a binomial probability. The probability of getting r successes out of n trials, where the probability of success of each trial is p and probability of failure of each trial is q (where q = 1 - p), is given by: n!(pr)[q(n-r)]/r!(n-r)!. Therefore, we need to find the probability of getting 10, 11,12,13,14,15 successes and add them up. Here, n=15, p=0.6, and q=0.4. r changes from 10 to 15.
p(11 successes) = 15!(0.611)(0.44)/11!(15-11)! = 0.1268
p(12 successes) = 0.0634
p(13 successes) = 0.0219
p(14 successes) = 0.0047
p(15 successes) = 0.00047
p(10 successes) = 15!(0.610)(0.45)/10!(15-10)! = 0.1859
p(11 successes) = 15!(0.611)(0.44)/11!(15-11)! = 0.1268
p(12 successes) = 0.0634
p(13 successes) = 0.0219
p(14 successes) = 0.0047
p(15 successes) = 0.00047
The sum of all the probabilities is 0.403.
User Contributed Comments 4
| User | Comment |
|---|---|
| haarlemmer | yes, if you'd take the risk. obviously the answer could either be b or d. assuming d is not, b therefore is the answer |
| steved333 | yeah, ya might want to take the risk on this one then come back to it if there's time. this one takes a little while... |
| endurance | Obvious very time consuming at exam - you are asked for P(10 or more) - then, you need only to calculate P(10)which is 0,186 and resonate that the prob is higher than B. |
| zed888 | endurance - one of the answers is 'none of these answers' - so you're taking a 50/50 guess |