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?
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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.