Question: A multiple-choice quiz has 10 questions. Each question has five possible answers, of which only oneis correct.(a) What is the probability that sheer guesswork will

A multiple-choice quiz has 10 questions. Each question has five possible answers, of which only oneis correct.(a) What is the probability that sheer guesswork will yield at least 9 correct answers?(b) What is the expected number of correct answers by sheer guesswork?(c) Suppose that 10 points are awarded for a correctly answered question. How many points shouldbe deducted for an incorrectly answered question, so that for a student guessing randomly, theexpected score on a question is zero? (Most standardized tests use this met hod to set penaltiesfor guessing).(d) If a student is able to correctly eliminate one option as a possible correct answer but is stillguessing randomly, what happens to his/her expected score for that question? Use your answerto (c) as the number of points being deducted for an incorrect answer.

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