Table 1

Expected gain due to random guessing after eliminating incorrect distractors in a multiple-choice question with five possible answers

Guessing StatusQuestion CategoryaProbability Expected Gain Due to Guessing
CorrectIncorrectpD=−1/4
pR=3/8
pD=−1/3
pR=1/3
pD=−1/2
pR=1/4
pD=−1
pR=0
Randomδ=41/54/50−0.067−0.2−0.6
δ=31/43/40.0630−0.125−0.5
δ=21/32/30.1670.1110−0.333
δ=11/21/20.375b0.333b0.25b0b
  • a δ represents the number of functioning distractors; thus, the student makes final selection of response to question from among the functioning distractors and the correct answer.

  • b Equal to reward.

  • Note: A student is assigned a score of +1 for a correct answer, −pD deduction for an incorrect answer, and pR if unanswered (i.e., the student recognizes and admits that he or she does not know).