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Here is a scenario: We have an MCQ exam with 100 questions.

Every 3 wrong answers will remove 1 correct answer.

The Minimum needed score to pass this exam is 50

I'm using the following formula : score = ( (correct * 3) - wrong) / (3 * total)) * 100;

now, I will calculate the student's score on each question, at what point should I decided that this student will not pass the exam no matter what he would do on the remaining questions?

I have not slept for almost 96 hours and I can't think clearly at this point

far2005
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1 Answers1

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If the student answers all the questions, and the number of questions answered correctly is $r$ and the number answered incorrectly is $w$ we have $$r+w=100$$ and in order to pass, the student needs $$r-\frac w3\geq50$$ Eliminating $w$ gives $r\geq 62.5$ and since $r$ must be an integer, we have $r\geq63$, which implies $w\leq37$. When the student has answered $38$ questions incorrectly, there is no possibility that he will pass.

The foregoing only applies if the student answers all the questions, but a student may skip some questions. I think the easiest thing to do is to keep a running score. If the student has answered $r$ questions correctly, $w$ incorrectly, and skipped $s$ questions, his score up to this point is $$r-\frac w3$$ and there are $100-r-w-s$ questions remaining, so the highest score he can possibly achieve is $$r-\frac w3+100-r-w-s=100-s-\frac{4w}{3}$$ If this is less than $50$, the student has no chance. Furthermore, the minimum number of questions he must answer correctly in order to pass is $50$ minus his current score, round up to the next integer, if necessary.

For example, suppose the student has seen $60$ questions, answered $40$ correctly, skipped $15$, and answered $5$ wrong. The student's score to this point is $$40-\frac53=38.333$$ so the student needs to answer at least $12$ more questions correctly.

If it were me, I would be reluctant to tell a student, "You must answer at least $12$ more questions correctly in order to pass," for fear he would interpret it, or at least say he interpreted it, as "If you answer at least $12$ more questions correctly, you will pass," which isn't true, since he might answer $12$ right and $28$ wrong. I would rather show the current score and the number of questions remaining. Then if a student sees that his current score is $40$ and there are only $9$ questions remaining, he will easily understand that he has no possibility of reaching $50$ and passing.

saulspatz
  • 53,131
  • Thank you, now is there a way to calculate his chance that he would pass before answering the 38th wrong question? – far2005 Dec 17 '20 at 01:14
  • Not unless we know the probabilities of his answering the questions correctly. You can't just calculate probabilities out of thin air. – saulspatz Dec 17 '20 at 01:15
  • What if we assume that he would give the correct answer? – far2005 Dec 17 '20 at 01:16
  • What does that mean? Correct answer to what? The next question? All the subsequent questions? I say it again. Unless we know the probabilities of his answering the various questions correctly, there is no way of computing the probability of his passing. I may also say, that if I were a student, and I found out that you had terminated my exam when there was still a possibility, however slight, that I could pass, I would be very angry indeed, and I would take whatever avenues were open to me to make you regret it. – saulspatz Dec 17 '20 at 01:20
  • at this point you are my hero don't get me wrong, to answer you, yes let's assume that he would give the correct answer to all the subsequent questions. I want to show him the chance that he would pass the exam. – far2005 Dec 17 '20 at 01:23
  • Ah, I understand finally. I'll add some more detail to my answer. – saulspatz Dec 17 '20 at 01:24
  • You are a legend, thank you – far2005 Dec 17 '20 at 01:25
  • Oops, one more thing. Is he allowed to skip a question? So that it counts neither for him nor against him? – saulspatz Dec 17 '20 at 01:27
  • yes he can skip a question – far2005 Dec 17 '20 at 01:27
  • I'm going to have to revise my answer then, because we don't have $r+w=100.$ It may be a little while. – saulspatz Dec 17 '20 at 01:30
  • I don't how to thank you at this point! this means a lot for me – far2005 Dec 17 '20 at 01:31
  • Thank you very much, I got what i needed. wish i could buy you a beer – far2005 Dec 17 '20 at 01:59