Question

Few students manage to complete their schooling without taking a standardized admissions test such as the Scholastic Achievement Test, or SAT (used for admission to college); the Law School Admissions Test, or LSAT; and the Graduate Record Exam, or GRE (used for admission to graduate school). Sometimes, these multiple-choice tests discourage guessing by subtracting points for wrong answers. In particular, a correct answer will be worth +1 point, and an incorrect answer on a question with five listed answers (a through e) will be worth −1/4 points.
What is the expected value of eliminating one answer and guessing among the remaining four possible answers?
What is the expected value of eliminating three answers and guessing between the remaining two possible answers?

Answer 1

Answer:

Step-by-step explanation:

Assuming there is a punitive removal of one point for an incorrect response.

Five undiscernable choices: 20% chance of guessing correctly -- Expectation: 0.20*(1) + 0.80*(-1) = -0.60

Four undiscernable choices: 25% chance of guessing correctly -- Expectation: 0.25*(1) + 0.75*(-1) = -0.50

I'll use 0.33 as an approzimation for 1/3

Three undiscernable choices: 33% chance of guessing correctly -- Expectation: 0.33*(1) + 0.67*(-1) = -0.33 <== The approximation is a little ugly.

Two undiscernable choices: 50% chance of guessing correctly -- Expectation: 0.50*(1) + 0.50*(-1) = 0.00

And thus we see that only if you can remove three is guessing neutral. There is no time when guessing is advantageous.

One Correct Answer: 100% chance of guessing correctly -- Expectation: 1.00*(1) + 0.00*(-1) = 1.00