Suppose an exam consists of multiple-choice questions, with each question having

Question

Suppose an exam consists of multiple-choice questions, with each question having 5 options. Exactly one of the five options is the correct answer. Suppose 20 points are awarded for a correctly answered question.

a) How many points should be deducted for an incorrectly answered question, so that for a student guessing randomly, the expected score on a question is zero?

b) If a student is able to correctly eliminate one option, as a possible correct answer but is still guessing randomly, what happens to his/her expected score for that question. Use the answe from a) as the number of points being deducted for an incorrect answer.

Explanation / Answer

a) p(correct answer)=1/5=0.2. If 5 points are assigned for correctly answered question and x=score for wrong answer E(score) = 0.2*5 + 0.8x = 1 + 0.8x =0 therefore s = -1.25 we should deduct 1.25 points for each incorrect answer

b) Student will now be guessing from 4 options instead of 5 so probability will be 1/4 of choosing the rght answer, thus p(correct answer)=1/4 =0.25

E(score) = 0.25 * 5 + 0.75 * (-1.25) = 0.3125

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