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September 15th, 2014, 09:35 AM  #1 
Senior Member Joined: Oct 2013 From: New York, USA Posts: 600 Thanks: 82  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*(Z1)^X?

September 15th, 2014, 11:41 AM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 937 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms 
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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