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**CFA Practice Question**

Carlson Jewelers permits the return of their diamond wedding rings, provided the return occurs within two weeks of the purchase date. Their records reveal that 10 percent of the diamond wedding rings are returned. Five rings are bought by five different customers. What is the probability that none will be returned?

A. 0.590

B. 0.372

C. 0.073

**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 = 5, r = 0,p = 0.10 and q = 0.90. Therefore we have 5!(0.1

_{0})(0.9

_{5})/0!5! = 0.590.

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**User Contributed Comments**
5

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

G3cc0 |
this question can also intuitavely be calculated at .9^5=.590 |

patra |
thanks G3cc0! |

takor |
G3cc0; 0.9^5 is not intuition. It is an algebraic reduction of the binomial term at last line of the explanation above.Intuition assists mastery of the concepts? |

apiccion |
nCn = 0Cn = 1 |

jjhigdon |
Note that C3cc0's shortcut only works if the r in nCr is 0. If it's not (e.g. what is the pobability that 3 or 4 or two or less, etc get returned?), you need to know the full binomial probability fomula. |