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There are totally $6$ students in the class. $5$ students have written the test and 1 student was absent. The test was for $40$ marks. Out of $5$ students, a student ‘Ram’ topped the class with $32$ marks. The course instructor announced that he topped the exam. The student who was absent for the test is writing the test tomorrow. What is the probability of this student to become a topper?

Ans 1: As there are $6$ students in the class, we have found the topper out of remaining five, the probability of him being a topper is $1/6$ .

Ans 2: A student can get $0,1,2\ldots 40$ any of the marks out of $40$. When he gets more than $32$ he will be the topper. So the probability of him being the topper is $8/41$.

Which answer is right? Or is there any other approach?

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migrated from mathematica.stackexchange.com Oct 5 '13 at 13:12

This question came from our site for users of Wolfram Mathematica.

  • $\begingroup$ If the absent student didn't open his/her books, the probability is very near to 0. Why should all marks be equiprobable? $\endgroup$ – egreg Oct 5 '13 at 13:24
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There can be no meaningful answer, given only the information provided. That information fails to address the degree of difficulty of each mark, or the comparative difficulty of one mark with another, the skill level of the students, the amount of time each student put into studying, the class attendance rate of each student prior to the exam, or the distribution of marks earned by all five students.

So the problem as posted is ill-posed, and one can only make stabs at answering it by making certain assumptions, and as the assumptions that one adopts vary, so will the answer, though one's assumptions may still leave the problem ill-posed so as not to admit any particular answer.

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