What is the probability of giving the correct answer to a multiple-choice question with four possible answers?

When you arrive at your statistics class on a hot Thursday afternoon, your instructor surprise you with an unexpected quiz.

Unfortunately, you haven’t paid any attention to the lectures or literature in the past weeks. The test is multiple choice. It consists of 10 questions, each with 4 possible answers (A,B,C and D).

a) What is the probability of giving the correct answer to a multiple-choice question with four possible answers?

b) If you give random answers to the 10 questions, how many questions would you expect to have answered correctly? In other words, what is the Expected Value?

c) You will pass the test if you answer at least 8 out of 10 questions correctly. What is the probability that you pass the test?