Probabilities of Random Guessing

[JamesCreswell]

Hello,

I am a student in high school and I possesses 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?

 

[mathman]

You are correct in that the expected score will be the same in either case. The only advantage of picking the same choice would be a smaller deviation, assuming that the test was set up that the correct answers were set to be uniformly distributed.

 

[Stephen Tashi]

If instructor's method is a faster method of guessing than varying your choices, it would give you more time to consider the questions where you are not completely guessing. That additional time might improve your score. That's the only advantage I see in your instructor's approach.