Exercise 4 For customers purchasing a refrigerator at a certain appliance store, let A be the event that the refrigerator was manufactured in the U.S., B be the event that the refrigerator had an icemaker, and C be the event that the customer purchased an extended warrant. Relevant probabilities are: P(A) = 0.75 P(B| A) = 0.9 P(B | A') = 0.8 P(C|AnB)=0.8 P(C|AnB')=0.6 P(C|A'nB)=0.7 P(C|A'nB')=0.3 a] Compute P(AanC) b] Compute P(BC) c] Compute P(C) d] Compute the probability of a U3. purchase given that an icemaker and extended warranty are also purchased. Exercise 5 After all students have left the classroom. (1 statistics professor notices that four copies of the text were left under desks. As the beginning of the next lecture. the professor distributes the four books in a completely random fashion to each of the four students it. 2. 3. and 4] who claim to have left books. One possible outcome is that 1 receives 2's book, 2 receives 4's book. 3 receives his or her own book, and 4 receives l's book. This outcome can be abbreviated as [2. 4. 3.1). a] List all possible outcomes. b] Let X denote the number of students who receive their own book. Find the probability mass function for X. c] Show that X follows a valid probability mass function. d] Find P(X