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September 15th, 2014, 10:35 AM   #1
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Test Probability Without Numbers Question

Every question on a multiple choice test has 5 choices. If there are X questions and the probability of getting every question correct by randomly guessing is Y, what is the probability of getting every question wrong by randomly guessing in terms of X and Y. Is it Y*4^X? A wrong answer is 4 times more likely than a correct answer. Going farther, if the number of questions changes from 5 to Z, does it become Y*(Z-1)^X?
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September 15th, 2014, 12:41 PM   #2
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You don't have enough information to decide. Suppose that question 1 has 4 answer choices and question 2 has only 1. Then you chance of guessing all the answers right is 1/4 and your chance of guessing all questions wrong is 0. But if there are 2 choices for each question then the chance of getting all questions right is still 1/4 but the chance of getting all wrong is 1/4 instead of 0.

But if you suppose that each question has the same number of choices, or more generally has the same probability p of being right, then p = Y^(1/X) and so you can compute (1 - p)^X as the probability of getting all questions wrong.
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