The Math of Guessing on an Exam
An interesting article on guessing answers on the SAT.
And some commentary:
It’s actually not quite true to say you shouldn’t guess on the SAT. It’s true that students are advised not to take a totally wild guess, but normally if you can eliminate one or more of the available answers, then guessing is +EV.
The reason for this is that unlike many other standardized tests, the SAT penalizes incorrect responses. Most of the multiple choice questions have 5 potential responses. For such questions, a correct answer is worth one point, and an incorrect answer deducts 0.25 points. So the Expected Value of randomly selecting from five responses is: 1/5*(1) + 4/5*(-0.25) = 0. While the neutral EV here still represents better odds than you get in any casino game, students are normally advised to be risk-averse and take the guaranteed zero (by leaving the answer blank) rather than risk the 80% chance of losing a quarter point.
However, if you can eliminate one of the 5 answers as being definitively incorrect, the equation becomes EV positive: 1/4*(1) + 3/4*(-0.25) = +0.0625. Since in the long run you’re expected to improve your score by guessing in these circumstances, students are normally advised to embrace the variance and take the guess. Obviously, your odds continue to improve as you narrow the possible responses down further.
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