15. Suppose you have to take a quiz for a class that consists of three questions. Each question has two choices, where one is correct and one is incorrect. You did not study, and you feel that you have an equal probability of getting any of the questions correct by guessing. You randomly choose one of the two answers for all three questions and hope for the best. (a) What is the probability distribution for O, the total number of questions answered correctly on the quiz. (9 points) (b) What is your expected number of correct answers on this quiz, based on your probability distribution in part a)? (3 points) (c) Suppose you have to answer at least 2 questions correctly in order to pass the quiz. What is the probability that you will pass? (3 points)