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I am a student in high school and I possess a keen proclivity for mathematics and physics. A contentious topic of discussion has come up among my friends, and I seek some assistance in resolving it.

A few days ago in my AP Chemistry class, the instructor told us that were we to have to guess on a multiple choice test, it would be advantageous to always pick the same choice (that is, consistently and solely choosing answer choice X for every question that must be guessed on will produce a higher expected score than will randomly selecting an answer choice for each question individually).

To this I object. Surely, regardless of the method of guessing employed, the expected score is always 20% (assuming 5 answer choices)? Am I incorrect? Can a proof or some sophisticated and impeccable logic be assembled on either side?

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# Probabilities of Random Guessing

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