Problem 9 On any given night, there is a 75% probability that you will watch a movie. Of the movies you watch, 60% are Good and 40% are Bad. Your decision to watch a movie or not, as well your choice of title, varies independently from night to night. (i) (4 pts.) Compute the probability that in the next ten nights, you will watch exactly three bad movies (and an unspecified number 0-7 of good movies). (ii) (4 pts.) Compute the probability that in the next ten nights, you will watch exactly three bad movies and five good movies. (iii) (4 pts.) Given that you watched a total of eight movies in the last ten nights, what is the conditional probability that exactly five of them were good? (iv) (1 pt.) (More involved) Given that you watched a total of eight movies in the last ten nights, what is the conditional probability that you watched exactly five good movies in the first seven nights? (v) (4 pts.) What is the probability that, starting tomorrow night, the first movie that you will watch will be a good one? (vi) (3 pts.) (Trickier) What is the probability that, starting tomorrow night, the first string of movies that you watch (i.c., followed by a no-movie night) will consist of good movies only