Benford’s law and distractors in multiple choice exams. (English)

Int. J. Math. Educ. Sci. Technol. 47, No. 4, 606-612 (2016).

Summary: Suppose that in a multiple choice examination the leading significant digit of the correct options follows Benford’s Law, while the leading digit of the distractors is uniform. Consider a strategy for guessing at answers that selects the option with the lowest leading digit with ties broken at random. We provide an expression for both the probability that this strategy selects the correct option and also the generalization to the probability of selecting the option with the lowest $r$ significant digit string.