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!(pr)[q(n-r)]/r!(n-r)!. Here, n = 10, r = 0,p = 0.05 and q = 0.95. Therefore we have 10!(0.050)(0.9510)/0!10! = 0.599.

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