What is the correct answer to the following question given original problem statement in Description below?

Question

A person takes a multiple-choice exam in which each question has five possible answers. Suppose that the person has no idea about the answers to three of the questions and simply chooses randomly for each one.

Suppose that the person gets one point of credit for each correct answer and that

1/3 point is deducted for each incorrect answer. What is the expected value of the person's score for the three questions?

Answer 1

Possible outcomes C correct W wrong

3 questions Probability Score

C C C 0.2 X 0.2 X 0.2 3

C C W 0.2 x 0.2 x 0.8 2 - 1/3

C W C 0.2 x 0.8 x 0.2 2 - 1/3

C W W 0.2 x 0.8 x 0.8 1 - 2/3

W CC

W C W

W W C

W W W

Write out the probabilities and the scores for the other 4 combinations

Multiply the probabilities by the scores

Add up these 8 results