SOLUTION: An exam consists of 20 multiple choice questions, each with 5 answer choices. If a student guesses on every question, this a binomial experiment with the random variable X

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Question 1204338: An exam consists of 20 multiple choice questions, each with 5 answer choices. If a student guesses on every question, this a binomial experiment with the random variable

X
=
Number of questions answered correctly
What is the probability that the student answers exactly 4 questions correctly?
Answer by ikleyn(53956) About Me  (Show Source):
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An exam consists of 20 multiple choice questions, each with 5 answer choices.
If a student guesses on every question, this a binomial experiment with the random variable
X
=
Number of questions answered correctly
What is the probability that the student answers exactly 4 questions correctly?
~~~~~~~~~~~~~~~~~~~~~ 

For each question, the probability to answer correctly is  4%2F5 = 0.8;
the probability to answer incorrectly is  1%2F5 = 0.2.


Since this experiment is binomial, the probability under the problem's question is

    P(4 of 20) = C%5B20%5D%5E4%2A0.8%5E4%2A0.2%5E%2820-4%29 = 4845%2A0.8%5E4%2A0.2%5E16 = 1.30057E-08.  


ANSWER.  P(4 of 20) = 1.30057E-08.

Solved.