Sports betting has become very popular lately. Suppose the following scenario and answer the questions. Three soccer games are going to be taking place between Romania and Korea in the following week. (a) What could logically happen, assuming that the games are clean (i.e., nobody paid Rumania or Korea to lose the game on purpose)? List all possible outcomes, defining your notation first. (b) Consider the events: A, which denotes the event that Korea wins two games B, which denotes the event that Romania wins at least two games C, which denotes the event that Korea wins three games D, which denotes the event that Romania wins at most one game. Do these events form a partition of the sample space? Why? Why not? Note: work is incomplete if you do not check all conditions. (c) Suppose the probability that Romania wins a game against Korea is 0.4 (given past history). Put together the probability mass function for the number of games won by Romania. Define your variables properly. Provide a probability mass function table that shows how you calculate the probabilities and the events that you are calculating probability for in each row of yourtable. Do not attach any files and do not provide links. Write your answers in the space provided