The government is attempt ing to determine whether immigrants should be tested for a contagious disease. Let’s assume that the decision will be made on a financial basis. Assume that each immigrant who is allowed into the country and has a disease cost the government $100,000, and each immigrant who enters and does not have the disease will contribute $10,000 to the national economy. Assume that 15% of all potential immigrants have the disease. The government may admit all immigrants, admit no immigrants, or test immigrants for the disease before determining whether they should be admitted. It cost $100 to test a person for the disease; The result is either positive or negative. If the test result positive, the person definitely has the disease. However, 25% of all people who do have the disease test as negative in the test . A person who does not have the disease always test negative. The government goal is to maximize expected benefit minus expected cost. a) Use a decision tree to determine the best strategy b) Write probability tree to obtain conditional probabilities ?(?|?) = ?(?|?) ∗ ?(?) ?(?) = ?(?) ∩ ?(?) ?(?)
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