Question 1 [14 Points] Movies at a theatre can be rated 1 star, 2 stars, 3 stars, 4 stars or 5 stars, all with an equally likely chance. Assume you go to this theatre to see two movies successively. Then you go back home to check the ratings of these two movies. a) [2 points] Write out the sample space of all outcomes of the ratings of the two movies (e.g. outcome "12" means the rating of the first movie is 1 star and the rating of the second one is 2 stars). b) [3 points] Let A be the event that both movies have the same rating. List the outcomes in A. What is P(A)? c) [3 points] Let B be the event that one movie is rated 2 stars higher than the other movie. List the outcomes in B. What is P(B)? d) [3 points] Let C be the event that the first movie has a lower rating than the second movie. List the outcomes in C. What is P(C)? e) [3 points] Are events A & B disjoint events? What does this tell you about the P(A or B)? Calculate P(A or B).