- 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**

An insurance agent has appointments with 4 prospective clients tomorrow. From past experience, the agent knows that the probability of making a sale on any appointment is 1 out of 5. Using the rules of probability, what is the likelihood that the agent will sell a policy to 3 of the 4 prospective clients?

A. 0.410

B. 0.250

C. 0.026

**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 = 4, r = 3,p = 0.20 and q = 0.80. Therefore, we have 4!(0.2

^{3})(0.8

^{1})/3!1! = 0.026.

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**User Contributed Comments**
3

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

Xocrevilo |
Given that the salesmen has a 20% (1 in 5) chance of success of any one sale, then the chance of making more than one sale must be less than 20%. Therefore, answers A & B both look too high. |

Kuki |
good observation by Xocrevilo which could save valuable time! |

8thlegend |
Can someone show me how to solve this algebrically(?) ? |