The Scantron Dilemma
Abraham and Julian have forgotten to study for their calculus final and must guess on every question. The test is multiple-choice and each question has only 4 answer choices A, B, C, and D with only one being the right answer.
Abraham remembers hearing that he should guess the same letter in order to maximize his chance of getting the answer right. As a result, Abraham answers choice C for every question on the test.
Julian on the other hand figures that each question has a 25% chance of being correct and therefore it shouldn't matter which answer choice he chooses. As a result, Julian answers a completely random letter for every question.
Whose method of guessing is better?
Assume that Julian's answer to each question is selected randomly, independent of his answers to other questions.
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1 solution
Despite popular opinion, Both methods are equal because as stated by Julian in the question each choice has a 25% chance of being correct.
The key to this problem is that each question's answer is independent from the others. Many students and teachers believe that it is best to stick by one answer choice but this is based on the assumption that one out of every four choices is guaranteed to be a specific letter (for example one out of every four is guaranteed to be C). However, on a perfectly randomized test this assumption isn't valid.
The next time you need to guess it's best to not overthink it and waste time optimizing your guessing strategy and actually solve the problem. 😊