1. Home Insurance - An insurance company charges an annual premium of $1050 for a homeowner's policy that will pay for at most one accident per year. For a catastrophic accident, the policy pays the maximum value of the house, $450,000, for a major accident, the policy pays $25000, for a minor accident, the policy pays $5000. The $1050 premium is not returned. The company estimates the probability of a catastrophic accident is .0005, for a major accident, .005 and for a minor accident, .08. What is the expected value of the policy to the insurance company? Hurricane season is approaching and a hurricane hitting this house will cause a loss of the house and thus a full payout. For what probability of a catastrophic accident will the insurance company break even? (assume the other probabilities remain the same)