Could you help me to solve these three questions step by step? And some explanation?

(8) [15 marks] The SFU football team has probability 0.3 of winning against Tier 1 teams, probability 0.4 of winning against Tier 2 teams and probability 0.5 of winning against Tier 3 teams. Half the teams in the league are Tier 1 while a quarter of them are Tier 2 and a quarter of them are Tier 3. The odds of an event A is given by: Pr[A] Odds [A] = TM 0 What are the odds that the SFU football team wins against a randomly chosen team? [10 marks] 9 Given SFU wins the game, what is the probability that the opponent was a Tier 2 team? [5 marks] (9) [25 marks] Prove the following statements. 0 For an event A and two mutually exclusive events E1 and E2, Pr[E1 U E2|A] = Pr[E1|A] + Pr[E2|A] implying that the union-rule for mutually exclusive events also works if we condition on the event A. [10 marks] 0 For an event A and two mutually exclusive events E1 and E2, prove the following statement. [10 marks] PI'[A]E1] PI'[E1] -]- PI'[A]E2] PI'[E2] P A E E = T[ I 1 U 2] PI'[E1] + ma] 9 Prove that the above rule generalizes the law of total probability, i.e. if E1 U E2 = S, then the above equation recovers the law of total probability, i.e. Pr[A] = Pr[A|E1] Pr[E1] + Pr[A|E1'3] Pr[Ef]. [5 marks] (10) [20 marks] Suppose that an insurance company classies people into one of three classes good risks, average risks, and bad risks. Their records indicate that the probabilities that good, average, and bad risk persons will be involved in an accident over a 1-year span are, respectively, 0.05, 0.15, and 0.30. If 20% percent of the population are \"good risks\