Expected point value for guessing?

Question

On a standardized exam, multiple choice questions with 5 possible answers are scored as follows: one point is awarded for correct response and (1)/(4)point is subtracted for each incorrect response. If the question is left blank, no points are added or subtracted. Calculate your expected point value if you guess on a question. On average is there anything to gain or lose by guessing?

Answer 1

x = correct answer

x' = incorrect

 

P(x) = 1/5 = .2

P(x') = 1-x = 1-.2 = .8

 

EV = P(x) * Value of x + P(x') * Value of x' 

= .2(1) + (.8)(-.25)

= .2 - .2

=0

 

Since your EV is 0, then there is nothing to gain or lose by guessing because it is neutral EV.

 

I actually went on a job interview a few years ago at an options trading company where just to get the interview you had to take a math exam just like this. You had to score at least 55 points out of 80 questions, but the catch was that wrong answers actually cost you 2 points instead of 1/4! In that case, guessing is grossly negative EV.