Question

In a multiple-choice test, each question has four options. Students will get 10 points for each correct answer; lose four points for each incorrect answer; and receive no points for unanswered questions. A student does not know the correct answer for one question. Is it to her advantage or disadvantage to guess an answer? Show your calculations for expected value. Show your work for full credit.

Answer 1

E[points rewarded for guessing] = (points for being right) * (probability of being right) + (points for being wrong) * (probability of being wrong) = 10*(1/4) - 4(3/4) = 10/4 - 12/4 = -1/2.

E[points rewarded for not guessing] = 0

0 > -1/2, so on average you're better off not guessing.