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 for choices that the student must eliminate before it is advantageous to guess among the rest

Answer 1

To make guessing advantageous, you want the average value of each question to be greater than 2 (since leaving is blank gives 2 points)

let's go through 1 by 1:
eliminate 0: 4/5 chance of getting it wrong (0) and 1/5 chance of getting it right (7), so on average you get (4/5*0 + 1/5 *7) = 7/5 points per question

eliminate 1: 3/4 chance of getting it wrong (0) and 1/4 chance of getting it right (7), so on average you get (3/4*0 + 1/4 *7) = 7/4 points per question

eliminate 2: 2/3 chance of getting it wrong (0) and 1/3 chance of getting it right (7), so on average you get (2/3*0 + 1/3 *7) = 7/3 points per question, which is greater than 2
->the student must eliminate 2 choices before guessing is advantageous