14. An instructor in an introductory economics class has constructed a multiple-choice test for the mid-term examination. The test consists of 20 questions worth 5 points each. For each question, the instructor lists four possible answers, of which only one is correct. John Partytime, a student in the class, has not attended class regularly, and admits (to himself) that he is really not prepared to take the exam. Nonetheless, he has decided to take the exam, and his strategy is to randomly choose one of the four answers for each question. He feels very confident that this course of action will result in an exam score considerably more than zero.

(a) Define a probability space that can be used to assign probability to events involving the number of questions that John answers correctly.

(b) What is the probability that John receives a zero on the exam?

(c) What is the probability that John receives at least 25 points on the exam?

(d) What is John’s expected score on the exam?