Question

In a multiple-choice test, each question has five options. Students will get 5 points for each correct answer; lose 2 point 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.

Answer 1

expected value of random choice: 1/5*5 + 4/5*(-2)=1-8/5

expected value of skipping, no answer: 0

so, skip it.

Now what if you could eliminate just one silly wrong answer?
expected value of guessing: 1/4*5-2(3/4)= 1.25-6/4=1.25-1.50=-.25

what if you could eliminate two silly answers....
expected value guessing=1/3*5 -2(2/3)= 5/3-4/3=.3333.

so, if you can't eliminate at least two answers, don't guess on this test. Normally on multiple choice, it is pretty easy to eliminate two answers.

Answer 2

oh okay...so confusing...thank you.