Question

Suppose you are taking a multiple choice quiz and have no idea how to answer. It awards you one point for a correct answer, and you get zero points for an incorrect answer, If you have to make a random guess and there are four possible answers, what is the expected value of guessing?

Answer 1

Point for correct answer = 1

Point for incorrect answer = 0

Number of possible answers = 4

P[ Correct answer ] = 1/4

P[ Incorrect answer ] = 1 - P[ Correct answer ] = 1 - 1/4

P[ Incorrect answer ] = 3/4

Expected value = P[ Correct answer ]*Point for correct answer + P[ Incorrect answer ]*Point for incorrect answer

Expected value = (1/4)*1 + (3/4)*0

Expected value = 1/4

Expected value = 0.25