Question 1204338
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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?
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<pre>
For each question, the probability to answer correctly is  {{{4/5}}} = 0.8;
the probability to answer incorrectly is  {{{1/5}}} = 0.2.


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

    P(4 of 20) = {{{C[20]^4*0.8^4*0.2^(20-4)}}} = {{{4845*0.8^4*0.2^16}}} = 1.30057E-08.  


<U>ANSWER</U>.  P(4 of 20) = 1.30057E-08.
</pre>

Solved.