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**CFA Practice Question**

On a very hot summer day, 5 percent of the production employees at Midland States Steel are absent from work. The production employees are to be selected at random for a special in-depth study on absenteeism. What is the probability of selecting 10 production employees at random on a hot summer day and finding that none of them are absent?

A. 0.344

B. 0.599

C. 0.002

**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 = 10, r = 0,p = 0.05 and q = 0.95. Therefore we have 10!(0.05

^{0})(0.95

^{10})/0!10! = 0.599.

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**User Contributed Comments**
11

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

G3cc0 |
you can also conceptualize this prob as P(not absent) = .95, so .95^10=.599 |

lwang014 |
I agree with G3cc0's method which is esaier |

DAS11 |
I also used P(not absent) |

itconcepts |
hey, if you managed to select them, they cant be absent, right? |

itconcepts |
ok, on a serious note, G3ccO's method must be a coincidence? if you had 100 employees you can't select 96 and still find none absent - while .95^96 will still give you a probability of .0073 ? |

itconcepts |
ok again, maybe not - the official formula gives the same result trying it with 96....hmmn, the flaw here is the sample size? |

malawyer |
@itconcepts: the number of workers is irrelevant in this case - it just asks of a sample size which is lower than the population-estimated absence |

Photon |
Thank you Analyst Notes |

jjhigdon |
The "short cut" method only works for all or none examples. If it were to ask for the probability of selecting 10 employees and finding 3 of them absent, you would need to apply the formula from the explanation. Further more it could ask for the probability that less than 3 or more than 7 of the 10 are absent, in which case you also need to know the proper formula... |

jjhigdon |
Which is much less confusingly stated as: nCr x P^r x (1-P)^n-r because you can quickly and easily use the calculator to solve nCr... |

ashish100 |
BA II (10 2nd nCr 10) * (.05)^0 * (.95)^10 = .5987 |