Some standardized​ tests, such as the sat​ test, incorporate a penalty for wrong answers. for​ example, a​ multiple-choice question with five possible answers will have 1 point awarded for a correct answer and​ 1/4 point lost for an incorrect answer. find the expected number of points​ (mean) received for a​ multiple-choice question with five possible answers when a student just guesses at random.

The expected value will be 0.

If a student is just guessing at random, she can expect to get 1 right out of 5.
That will give her 1 point.

Then, she can expect to get 4 questions wrong. If we multiply 1/4 by 4, we get a total of 1 point.

She will gain a point and lose a point making her expected value zero.