Each question on a multiple-choice exam has four choices. One of the choices is correct, worth four points. Another choice is wrong but carries partial credit of one point. The other two choices are wrong and worth negative one point. If a student picks answers at random, what is the expected value of his or her score for a problem?
A)0.25
B)1.25
C)0.75
D)1.50

Question

Quizplus · Accepted Answer

The expected value is the sum of each possible outcome multiplied by its probability. Out of the four choices, there are two bad outcomes ($-1$) and one partially correct outcome ($+1$), each with a probability of $1/4$. The probability of the correct outcome is also $1/4$, but it is worth $4$ points. Thus, the expected value is: $$\frac{1}{4}(4)+\frac{1}{4}(1)+\frac{1}{4}(-1)+\frac{1}{4}(-1) = \frac{3}{4} = 0.75$$ Thus, the best choice is (C).

Each Question on a Multiple-Choice Exam Has Four Choices