Probability Problem?

Question

A Multiple choice test has 4 possible answers to each of 20 questions. If a correct answer to a question will earn 4 marks and an incorrect answer is given a penalty. What is the appropriate penalty so that the test is fair? (Full solutions will be appreciated thanks.)

I know that a test is fair when the expected score is 0.

Answer 1

最愛解答

4*(1/4)-penalty*(3/4)=0

penalty=4/3 (marks).....Ans