An instructor in an introductory economics class has a true-false section on the mid-term examination that consists of 10 questions worth 3 points each. Jeff Nostudy, a student in the class, has not attended class regularly, and knows that he is really not prepared to take the exam. Nonetheless, he decides to take the exam, and his strategy is to treat true and false as equally likely for each question, and randomly choose one as his answer to each question. He feels very confident that this course of action will result in a score for the true-false section that will be considerably more than zero.

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

(b) What is the probability that Jeff receives zero points on the true-false section of the exam?

(c) What is the probability that Jeff receives at least 15 of the 30 points that are possible on the true-false section of the exam?

(d) What is Jeff's expected score on the true-false section of the exam?