posted by Jen on .
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.
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.
oh okay...so confusing...thank you.