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A manufacturer has two expansion options available to him. The profits of the expansions depend on the cost of energy. The fair odds are 3:2 in favor of energy costs being greater than 8/kwh. The manufacturer is twice as likely to choose option 1 as option 2, regardless of circumstances. If the cost of energy is less than 8/kwh, then expansion option 1 will yield returns of +$150,000, $0, and - $50,000 with probabilities of 60%, 20%, and 20%, respec- tively. Under those conditions, expansion option 2 will yield returns of +$100,000, +$20,000, and -$20,000 with probabilities of 70%, 10%, and 20%, respectively. If the cost of energy is greater than 8/kwh, then option I will yield returns of +$100,000, SO, and -$50,000 with probabilities of 60%, 20%, and 20%, respectively, while option 2 will yield returns of +$80,000, $0, and -$50,000 with probabilities of 70%, 10%, and 20%, respectively. a) What is the probability that option 2 will be pursued and that energy prices will exceed 8/kwh? b) What is the manufacturer's expected return from expansion? c) Given that several years later the expansion yielded a return greater than zero, what is the probability that option 2 was chosen