SOLUTION: Research finds that of the students entering a degree program, 90% will successfully complete it. In 2018, 15 students commenced the course. Calculate the probability that: I) al

Algebra ->  Statistics  -> Binomial-probability -> SOLUTION: Research finds that of the students entering a degree program, 90% will successfully complete it. In 2018, 15 students commenced the course. Calculate the probability that: I) al      Log On


   

Question 1193467: Research finds that of the students entering a degree program, 90% will successfully complete it. In 2018, 15 students commenced the course. Calculate the probability that:
I) all 15 students will successfully complete the course.
II) only one student fails.
III) no more than two students fail.
I) at least two students fail.
Answer by ikleyn(53956) About Me  (Show Source):
You can put this solution on YOUR website!
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Research finds that of the students entering a degree program, 90% will successfully complete it.
In 2018, 15 students commenced the course. Calculate the probability that:
I) all 15 students will successfully complete the course.
II) only one student fails.
III) no more than two students fail.
I) at least two students fail.
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            All these problems/questions are about binomial probability distribution.
            So,  use the related standard formulas. 


(i)    P = 0.9%5E15 = 0.2059   (rounded).    ANSWER



(ii)   P = C%5B15%5D%5E1%2A0.9%5E14%2A%281-0.9%29%5E1 = 15%2A0.9%5E14%2A0.1 = 0.34315   (rounded).     ANSWER



(iii)  "No more than two students fail" means 0, 1, or 2 students fail


       P = P(0 fail) + P(1 fails) + P(2 fail) = 

         = 0.9%5E15 + C%5B15%5D%5E1%2A0.1%5E1%2A0.9%5E14 + C%5B15%5D%5E2%2A0.1%5E2%2A0.9%5E13 = 

         = 0.9%5E15+%2B+15%2A0.1%2A0.9%5E14+%2B+%28%2815%2A14%29%2F2%29%2A0.1%5E2%2A0.9%5E13 = 0.8159    (rounded).    ANSWER



(iv)  "at least two students fail" means that no more than 1 student pass


       P = P(0 pass) + P(1 passes) = 0.1%5E15 + 15%2A0.9%5E1%2A0.1%5E14 = 0.1%5E15+%2B+15%2A0.9%2A0.1%5E14 = 1.36*10^(-13).     ANSWER

Solved.