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## Probability teaser

 Quote by Constantinos *Let's suppose that A is the correct answer. Then D is the correct answer also, since they state the same thing. Are my assumptions wrong? Is the solution wrong?
This assumption is incorrect. For example, take questions #6 and #17 of this test. B/D and D/B would seem to be correct answers for both questions, but there is only one correct answer for each question.

You need the entire test to know for sure whether A or D (or both) is the correct answer. Depending on the context, a random choice could still have only a 25% chance of being correct, even when two choices list the same answer - and even if there's not enough information provided to know which choice listing 25% is the correct answer.

Edit: However, there does have to be some assumption made in order for there to be a correct answer. For example, there are 26 letters in the English alphabet, 28 in the Spanish alphabet, and 33 in the Cyrillic alphabet. Since the question is written in English, assuming they're talking about picking a random letter in the English alphabet would be a good assumption - except picking a random letter would have less than a 25% chance of being correct - meaning there must be some other limiting assumptions made, as well.
 Admittedly, although they specify "random", they don't actually specify that the randomness is evenly distributed. It could be random with a bias, in which case it's not possible to determine the answer, despite the fact that there might be a correct one. DaveE
 Recognitions: Gold Member Homework Help Science Advisor Forensic analysis indicates the correct answer must be A. All of the numbers except one were written by the same person. The handwriting style of the '2' in answer D is different than the handwriting style used for the other numbers. Additionally, most of the erasure marks on the board match the circular motion used to erase a large amount of data. The almost straight line erasure mark coming from the '2' in answer D indicates a very small amount of data was erased while taking care not to erase other data. Furthermore, proper testwriting technique requires the choices to be written in some sort of logical order: shortest to longest, longest to shortest, smallest to largest, etc. A, B, and C are properly formatted with each answer giving a higher percentage, and then D suddenly presents a lower percentage. D clearly was originally 65%, 75%, 85%, or 95%. Answer D was altered to maliciously mislead the masses.