Question 1129379: Please help. A multiple choice test has 20 questions. Each question has five possible answers, of which one is correct. If a student guesses on every question, find the probability of getting 12 correct.
Found 2 solutions by ikleyn, solver91311:
Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website! .
Imagine that for each of the 20 multiple choice questions the answers are labeled by 5 letters A, B, C, D and E
(5 possible answers to each question).
By answering to each question, you mark your answer by one of the 5 letters.
So, by answering to 20 questions, you write the word of the length 20, using one of 5 letters in each of the 20 positions.
It is your model. The entire space of events consists of all  such words of the length 20, written in 5-letter alphabet.
Now I am ready to answer the problem's questions.
If a student guesses on every question, find the probability of getting 12 correct.
So the student put correct marks (selects correct letter answer) in 12 cases and selects incorrect letter answers in 20-12 = 8 cases.
Giving incorrect answers, the student has 4 opportunity for each multiple choice questions, or, in all,  possibilities.
Thus the probability under the question is this value
 =  = 8.65E-5 =  = 0.0000865 (approximately).
Answer by solver91311(24713)  (Show Source):
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