Few students manage to complete their schooling without taking a standardized admissions test such as the Scholastic Achievement Test, or S. A.T. (used for admission to college); the Law School Admissions Test, or L. S.A. T.; and the Graduate Record Exam, or G. R.E. (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
4point.
(a) Find the expected value of a random guess.

(b) Find the expected value of eliminating one answer and guessing among the remaining four possible answers. (Enter an exact number as an integer, fraction, or decimal.)

(c) Find the expected value of eliminating three answers and guessing between the remaining two possible answers. (Enter an exact number as an integer, fraction, or decimal.)