Question

A quiz has multiple-choice questions, each with 5 choices. The answer possibilities are distributed evenly. If a student gets a correct answer they will receive +3 points. If they leave it blank, they will receive 0 points. If they write an incorrect answer, they will receive -1 point. A student guesses the answers to some questions.
Determine on average, in the long run, how many points the student will score. (Write your answer as a decimal, with a minus sign if needed.)
a0 points per question

Answer 1

The probability of choosing a correct answer = 1/5
The probability of choosing a wrong answer = 4/5

Scores received on correct answer = +3
Scores received on wrong answer = -1

The average scores, in long run will be equal to the expected value. The expected value E, in this case will be:

$E= \frac{1}{5}(3)+ \frac{4}{5}(-1)=-0.2$

Thus, in long run, the student will score -0.2 points on average.