Question

Suppose in a multiple choice type test, each question has five choices. To discourage students from guessing the correct answer, the following scoring method is used: 7 points for correct answer, 0 point for wrong answer, and 2 points for leaving the question unanswered.   What is the minimum number of choices in each question a student should be able to eliminate, so that it becomes advantageous to guess from the remaining choices?

choice: 1 2 3 4

Answer 1

Let the number of options be k.

Then the probability of getting the correct answer = 1/k

Thus, the average score obtained while attempting an answer = 7 * (1/k) + 0 * (1-1/k) = 7/k.

The average score obtained without attempting an answer = 2.

Hence, in order it becomes advantageous to guess from the remaining choices, 7/k > 2 i.e. k < 3.5

The highest possible integer value of k is 3.

Currently, we have five choices for each question.

Hence, a student should eliminate (5-3) = 2 options.