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There is a 120-choice quiz with 5 choices. From the first question, the student marks the questions as e, a, c, c, d, e, a, c, b, c, d, e... What is the probability that this student will answer 7 questions correctly in the exam?

a- 17 times b- 17 times c- 51 times d- 17 times e- 18 times

The student repeats answers every 7 times. He does the same operation 17 times and the answer to the last question is e. Already 120 = 17.7 + 1. Well, I can't figure out how to solve this question because there's a repeat. Thanks for your help.

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    $\begingroup$ Are we to assume that the correct answers are uniformly distributed and independent of the responses? If so, then it makes no difference what the student answers, each choice is equally likely to be correct or incorrect. $\endgroup$ – lulu Jan 14 at 11:28
  • $\begingroup$ I don't really know any more information about the question. In the answer key, the answer is 1/3. $\endgroup$ – Dore Jan 14 at 15:17
  • $\begingroup$ Well, that answer is certainly not compatible with the assumption that the true answers are distributed randomly. More information is needed. $\endgroup$ – lulu Jan 14 at 15:22
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I'm assuming that the answers are uniformly distributed. Since the student is effectively choosing a random answer on each question I'd presume a probability of success of 0.2 (1 in 5) and use a binomial distribution to determine values of probability of getting x many answers correct.

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