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Here is my problem, there are 6 students suspected of cheating on a NJ Real Estate pre-licensing course exam. You must pass this course to take the NJ State exam, and for obvious ethical reasons we would rather not see these people get licenses! I need help figuring out the probability of them getting answers the same, regardless of right or wrong. Here is what I know:

There is one student, our control "Jane", suspected of changing other students' answers.

The test contains 110 questions with 4 answer choices per question

5 students have 94% to 98% of the same answers as Jane (Again, regardless of right or wrong). A fifth student has 85%

We are in the process of analyzing the other 30 exams for a frequency graph... so far they have roughly 50% of the same answers as Jane.

What is the probability of 2 students have 98% of the questions answered the same? 94% the same? We would like to be able to state it as a "one in x,000" sort of ratio.

I am somewhat proficient in stats, but I am hitting a brick wall on this one. If someone could show formulas and calculations I would be greatly appreciative!!

Thanks much!

Carolyn

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# Probability problem - Test Cheaters

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