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

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**CFA Practice Question**

In a large metropolitan area, records revealed that 30 percent of all high school graduates go to college. From 20 graduates selected at random, what is the probability that exactly 8 will go to college?

A. 0.231

B. 0.114

C. 0.400

**Explanation:**This is a binomial probability. The probability of getting r successes out of n trials, where the probability of success each trial is p and probability of failure each trial is q (where q = 1-p), is given by: n!(p

^{r})[q

^{(n-r)}]/[r!(n-r)!]. Here, n = 20, r = 8,p = 0.3 and q = 0.7. Therefore, we have 20!(0.3

^{8})(0.7

^{12})/[8!12!] = 0.114.

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**User Contributed Comments**
5

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

samerthehammer |
Shouldn't be 20 Combination 8 at the begining of the formula. |

shiva5555 |
20!/8!12! is the same as 20 combination 8. Just use the calculator its easier. |

dipu617 |
I'm getting "125,970" for 20 combination 8!!!! Any explanation????? |

cebus |
You probably missed some numbers when dividing |

safash |
Dipu that's rite 20C8* .30^8*.70^12 125970*.00006561*.01384129=.14437 |