Question

A mathematics competition uses the following scoring procedure to discourage students from guessing (choosing an answer randomly) on the multiple-choice questions. For each correct response, the score is 7. For each question left unanswered, the score is 2. For each incorrect response, the score is 0. If there are 5 choices for each question, what is the minimum number of choices that the student must eliminate before it is advantageous to guess among the rest?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Please include the procedure

Answer 1

Since there are 5 options, the probability of randomly guessing the correct answer is 1/5 or 0.2.

The expected marks scored when a student guesses an answer is 0.2*7 (7 is the marks received for a right answer) + 0.8*0.

= 1.4

On leaving the question unanswered , the student received 2 marks.

In this case, leaving the question unanswered is more advantageous since the expected marks on leaving a question is greater.

Similarly, on eliminating 1 option, the probability of success in a random guess changes to 0.25.

The expected score is 0.25*7=1.75 which is still less than 2.

Similarly, on eliminating 2 options, the probability of success in a random guess changes to 0.33.

The expected score is 0.33*7 = 2.31.

This is greater than 2.

Thus, the minimum number of choices that the student must eliminate before it is advantageous to guess among the rest is (C) 2.