# Finding the probabilities of each correct answer

Here is the word problem that I made up (this actually happened to me), and I would like to find out how I would work this. This problem seems to be rather hairy.

Suppose a teacher puts you into a group and hands you five papers. The following table describes the papers:

Number of Questions Missed:|Answers Chosen:
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5                          |A,B,C,D,B,C,E
3                          |A,B,C,D,B,C,E
4                          |A,B,C,D,B,C,E
5                          |A,B,C,D,B,C,E


Each paper has a certain number of questions missed, and each has the answers chosen above (the answers in the table are just an example, if you want actual sample data, just ask and I can easily fix the table to reflect a real scenario).

Given the above information, which answer is most probably correct for each question and what is the probability of it being correct?

Note: The above table is just to show the type of question that I am asking, as I am more interested in the methodology than the answer.

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If every paper has the same answers, how can they have different numbers of misses? – Henning Makholm Oct 23 '12 at 0:02