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cyco_cc · 12-04-2009, 04:53 PM

Suppose each question has the same number of choices, n. Let m be the number of questions.

So there are n^m possible test answer configurations which can be submitted with only 1 being 100% correct. The probability of choosing the right answer on any one question at random is 1/n. So, the probability of choosing x% correct answers at random is (100/x) * n^(-m).

So even with n=4 and m=20, the probability of guessing and getting 60% is 5/(3*4^20) which is a microscopic percentage.

This is assuming they are being chosen completely at random, though.

12-04-2009, 04:53 PM
cyco_cc Confirmed User Join Date: Oct 2008 Posts: 344	Suppose each question has the same number of choices, n. Let m be the number of questions. So there are n^m possible test answer configurations which can be submitted with only 1 being 100% correct. The probability of choosing the right answer on any one question at random is 1/n. So, the probability of choosing x% correct answers at random is (100/x) * n^(-m). So even with n=4 and m=20, the probability of guessing and getting 60% is 5/(3*4^20) which is a microscopic percentage. This is assuming they are being chosen completely at random, though.