There are 20 questions in a multiple choice exam, each with 4 answers and only one is correct. The students are guessing the answers in an independent way. Correct answer = +5, incorrect answer = -1, unaswered = 0. What is the expected value of the grades, what is the variance of the grades and what is the probabilty to get the same grade as the expected value?

The answers are: 10, 135, 0.2.
I tried binomic distrubiton: p = 0.125 (0.5 if the students choose to answer the question and 0.25 if they're right) but I don't get the correct answers.

Thank you.