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You live in an area that has a possibility of incurring a massive earthquake, so you are considering buying earthquake insurance on your home at an annual cost of $180. The probability of earthquake damaging your home in one year is 0.001. If this happens, you estimate that the cost of the damage (fully covered by earthquake insurance) will be $160,000. Your total assets including your home are worth $250,000. Also, you can check your house to see if it is earthquake safe or not for the cost of $50. Assume that the test is valid for one year and its result is not valuable after one year. From the historical data you know that the probability that a house which is damaged has been reported to be earthquake safe is 10%. Also, you know that the probability that a not damaged house has been reported not to be earthquake safe is 30%.

1. Develop a decision analysis formulation of this problem by identifying the decision alternatives, the states of nature, and the payoff table when the earthquake safety check is not conducted.
2. Assuming the earthquake safety check is not conducted, which alternative would you chose to minimize your maximum regret?
3. Assuming the earthquake safety check is not conducted, use Bayes decision rule to determine which decision alternative should be chosen.