I have an exam tomorrow with 100 multiple choice questions. Each question has 4 options, only 1 is correct.

If I answer the question and get it right, I get 1 mark. If I leave it blank, I get 0. If I answer incorrectly, I lose 0.25 marks.

How should one approach the test? Mathematically/statistically are my odds better if I guess if I don't know the answer?

  • $\begingroup$ What kind of test is this? The only test I've ever taken where they take marks off for incorrect answers is the SAT. $\endgroup$ – Chris K Dec 10 '13 at 4:35
  • $\begingroup$ I'm from Australia and it's an exam for a course I'm studying at uni. $\endgroup$ – user2342435 Dec 10 '13 at 9:16

Imagine if you had $4$ questions you don't understand.

If you leave them blank, you will get a mark of $0$.
If you guess all of them, the expected result is getting $1$ right and $3$ wrong. This will get you an expected mark of: $$1-3(0.25)=0.25$$

Therefore it is better to guess than to leave questions blank.

  • $\begingroup$ You need to divide your result by four... $\endgroup$ – Potato Dec 10 '13 at 6:41
  • $\begingroup$ This is for 4 questions and don't confuse the OP $\endgroup$ – Abraham Zhang Dec 10 '13 at 6:42
  • $\begingroup$ The question seems to be about individual questions, though. It's not obvious from this result that guessing is still the right move when confronted with 1,2, or 3 questions. $\endgroup$ – Potato Dec 10 '13 at 6:44
  • $\begingroup$ I'm just showing that is better to guess, this will account for every individual question $\endgroup$ – Abraham Zhang Dec 10 '13 at 6:46
  • $\begingroup$ You have shown that given 4 questions that the test-taker does not know the answer to, it is better to guess on all 4 than leave all 4 blank. This doesn't immediately generalize to the case of 1 question. $\endgroup$ – Potato Dec 10 '13 at 6:47

If you can eliminate at least one choice on a question, then you should guess from the remaining choices.

  • 1
    $\begingroup$ It would be nice to give a proof... $\endgroup$ – Potato Dec 10 '13 at 4:36
  • 2
    $\begingroup$ Also, maybe I'm making an error, but it seems like one should guess even if no answers can be ruled out. The expected value of guessing is $.25(1-.25-.25-.25)>0$, which is better than leaving it blank. $\endgroup$ – Potato Dec 10 '13 at 4:38
  • $\begingroup$ While I did not give a proof, it most certainly does answer the question as stated "How should one approach the test?" $\endgroup$ – Carl Love Dec 10 '13 at 5:04
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    $\begingroup$ @CarlLove What you say is true, but misleading. You should guess even if you can't eliminate an answer. $\endgroup$ – Potato Dec 10 '13 at 5:25
  • $\begingroup$ @Potato You're right about the expected value of guessing always being positive. $\endgroup$ – Carl Love Dec 10 '13 at 5:32

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