Each question on a multiple-choice exam has four choices.

Question

One of the choices is the correct answer, worth 5 points, another choice is wrong, but still carries partial credit of 1 point, and the other two choices are worth 0 points.

If a student picks answers at random, what is the expected value of his or her score for a problem?
points

If the exam has 30 questions, what is his or her expected score?
points

Answer 1

The probability for each answer is 1/4.

 

5(1/4) + 1(1/4) + 0(1/4) + 0(1/4)

5/4 + 1/4

6/4

2.25

 

Each question has an expected value of 2.25 points.

 

The expected value of the test is 30(2.25) or 67.5.