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In a multiple choice test consisting of 90 questions. Each question has four choices out of which 1 is correct. +4 for each correct and -1 for each incorrect answer. Should the optimal strategy be to guess all the answers one doesn't know as guessing more answer would get us closer to the expected value or should one play safe and not guess at all or guessing a certain number of questions would be optimal?

My attempt: By expected value, for each question: 4*1/4 - 1*3/4 = +1/4. Therefore for all 90 questions expected score would be +22.5 points. Best strategy should be to guess all. I don't know. Help.

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    $\begingroup$ This depends on what you're optimizing. If you want to maximize your expected value, guessing is a good idea unless you're short on time. If you want to maximize the probability that you hit a certain threshold, it may not be (depending on what that threshold is and how many questions you actually know the answer to). $\endgroup$ – Micah Mar 31 '17 at 18:18
  • $\begingroup$ If I want to score maximum points @Micah $\endgroup$ – novak Mar 31 '17 at 18:23
  • $\begingroup$ i want to get maximum score possibel. $\endgroup$ – novak Mar 31 '17 at 18:27
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Given a question with four answers to choose from, it may be that you don't know the correct answer but you do know that one of the answers is incorrect. In that case, by guessing among the remaining three answers you can improve your expected value on that question to $(4\times1/3) - (1\times 2/3)=2/3$ . Similarly, if you know that two of the answers are incorrect, you can improve your expected value to $(4\times1/2)-(1\times1/2)=3/2$ by guessing among the remaining two answers.

To maximise your expected value on the test, therefore, you should not only guess an answer to those questions where you have no idea, but also be on the lookout for questions where you know that one or two of the answers are incorrect and proceed as above.

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