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.