SOLUTION: A company finds that one out of every 8 workers it hires turns out to be unsatisfactory. Assume that the satisfactory performance of any hired worker is independent of that of any

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Question 1204066: A company finds that one out of every 8 workers it hires turns out to be unsatisfactory. Assume that the satisfactory performance of any hired worker is independent of that of any other hired workers. If the company hires 14 people, what is the probability that the following number of people will turn out to be satisfactory? (Round your answer to six decimal places.)
exactly 9
Answer by ikleyn(52763) About Me  (Show Source):
You can put this solution on YOUR website!
.

It is typical binomial distribution probability problem.


The number of trials is n= 14;
the probability of a successful individual trial is p= 7%2F8;
the number of success trials is 9.


Use the standard formula for the probability

    P = C%5B14%5D%5E9%2A%287%2F8%29%5E9%2A%281%2F8%29%5E%2814-9%29 = 2002%2A%287%2F8%29%5E9%2A%281%2F8%29%5E5 = 0.01837  (rounded).    ANSWER


This probability is low, because for this problem, the higher probabilities are for greater number of success.

Solved.

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To see many other similar  (and different)  solved problems,  look into the lessons
    - Simple and simplest probability problems on Binomial distribution
    - Typical binomial distribution probability problems
in this site.

Learn the entire subject from there.