4. In January of 2021, the magazine Variety reported that Netflix was introducing a new "shuffle play" feature to randomly choose something for viewers to watch. The article said the new feature would pick "either shows or movies similar to ones you've watched previously; titles in genres you've viewed; or content you have saved in the "My List" section." Suppose that for a particular viewer, 1000 videos in the Netflix database currently meet this description, and the shuffle feature is going to choose one of these 1000 videos at random. Some attributes of these videos are summarized in the following two-way table. Episode of Movie Total a show Fictional 509 312 821 Non-fictional 143 36 179 (e.g. reality shows documentaries) Total 652 348 1000 (a) What's the chance that the chosen video is an episode of a fictional show? (b) Given that the chosen video is fictional, what's the chance it is an episode of a show? (c) Are the events "getting a video that's a movie" and "getting a video that's non- fictional" mutually exclusive? Answer yes or no and justify your answer. (d) Are the events "getting a video that's a movie" and "getting a video that's non- fictional" independent? Answer yes or no and justify your