1. Your baseball team is playing a best-of-five scries, i.e a sequence of games in which the first team to win 3 games in total wins the entire scries. Think of thc whole scries as a random experiment and represent iLs outcorm*-; sequences of wins or losses (denoted by W/L) for your team. E.g., the outcome (W, L, W, W) means that your team won games and 11 (and last game 2), at which point your team won thc series. Notc that there are no mote games played after a team wins thc series. Define the events: A = { your team won three games in a mw B = { your team won the C the oppking team won at leu-st one game } Answer the following questions: (a) (2 points) List all the outcomns in event A. (b) (3 points) What is the relationship of events A and B: arc they disjoint, comple- mentary, or is one a subset of the other? Justify your answer. (e) (3 points) List all the outcomns in event (B n C). (d) (4 points) List all the outcomes in the sample space (Hint: there are 20 distinct outcomes) For the remaining questions, we probabilitil* to according to the fol- lowing scheme: As.;ume both teams have the same chances of winning each game, ir- respective of other games. This implies that the probability of an outcome is equal to (1/2), where is the sexies length- E.g., L, W, W)) = (1/2)' because there are games played in the series (W, L, W, W). This (lefine a probability function that assigns to any event E the sum of the probabilities of all outcomes in E: (e) (4 points) Find the value of thc probability P(A). (f) (4 points) Verify that P(S) 1, i.e. that this is a valid probability function.