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 What is

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Question 1204336: 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
What is the probability that the student answers exactly 4 questions correctly?

Answer by ikleyn(52790) 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
What is the probability that the student answers exactly 4 questions correctly?
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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.