Question

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

1.5

45

Explanation:

The probability for each answer is 1/4

• (5+1+0+0)/4 = 6/4= 1.5

Each question has an expected value of 1.5 points.

The expected score of the test is 30*1.5= 45 points