SOLUTION: There are five possible answers for each question in a multiple choice examination containing 12 questions. If a candidate answers the questions randomly, find the probability that

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Question 1207520: There are five possible answers for each question in a multiple choice examination containing 12 questions. If a candidate answers the questions randomly, find the probability that the candidate gets:
(a) no question right;
(b) nine questions wrong;
(c) at least one question right;
(d) not more than ten questions wrong.
Answer by ikleyn(53937) About Me  (Show Source):
You can put this solution on YOUR website!
.
There are five possible answers for each question in a multiple choice examination
containing 12 questions. If a candidate answers the questions randomly,
find the probability that the candidate gets:
(a) no question right;
(b) nine questions wrong;
(c) at least one question right;
(d) not more than ten questions wrong.
~~~~~~~~~~~~~~~~~~~~~~ 

Answering each multiply choice question has the probability

    to be right of 1/5 = 0.2;  to be wrong 4/5 = 0.8.


This experiment is binomial, such the probability of success 
is the same for each of 12 trials, and answering different multiply choice question
are independent events.

Having this in mind, let start.


(a)  P = %284%2F5%29%5E12 = 0.8%5E12 = 0.06872  (rounded).


(b)  Use the standard formula of binomial distribution

         P = C%5B12%5D%5E9%2A0.8%5E9%2A0.2%5E3 = 220%2A0.8%5E9%2A0.2%5E3 = 0.2362   (rounded).

             (9 wrong means 9 wrong, 3 correct).


(c)  at least one question right is the COMPLEMENT to "all answers are wrong".

         P(all answers are wrong) = 0.8%5E12 = 0.06872  (rounded).

               (it is what we calculate in a).

         Therefore, P(at least one question right) = 1 - 0.06872 = 0.93128.

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If you want to see many similar or different solved problems on binomial distribution probability,  look into the lessons
    - Simple and simplest probability problems on Binomial distribution
    - Typical binomial distribution probability problems
    - How to calculate Binomial probabilities with Technology (using MS Excel)
    - Solving problems on Binomial distribution with Technology (using MS Excel)
    - Solving problems on Binomial distribution with Technology (using online solver)
in this site.

After reading these lessons,  you will be able to solve such problems on your own,
which is your  PRIMARY  MAJOR  GOAL  visiting this forum  (I believe).