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Question: homework assignment 1 spring 2019 question 2 bayes rule a...

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Homework Assignment 1 Spring 2019 Question 2: Bayes Rule (a) A customer interested in a loan approaches the bank you work for. Based on historical information, the bank believes that the customer will be able to repay the loan with a probability of 97.5%. However, before they agree to provide the customer with a loan, the bank will run a credit check. Historically, 80% of the people that repay the loan had a good credit check: 15% of the people that repay the loan had al.werage credit check; finally, 5% of the people that repay the loan had a bad credit check. On a different note, only 2% of the people that did not repay their loans had a good credit check: 18% of the people that did not repay the loan had average credit, and 80% of the people that did not repay the loan had bad credit What is the probability that a person with a good background check fails to repay the loan? What is the probability that a person with a bad background check fails to repay the loan? (b) You are working for your local office of the FDA (the Food & Drug Administration) as a food security analyst. From your experience in the field, youve noticed that items of interest are often deemed one of four levels of risk for food consumption. These levels are no risk, mild risk, moderate risk, and major risk. The probability of these categories are (historically) P(no risk) 0.6 Pl moderate risk) = 0.15 Moreover, you are able to utilize your resources and analyze a foods chemical composition. This experiment is done after receiving authorization and determines if the food of interest is a possible threat to public consumption, or can be dismissed as not a threat. The probabilities of the experiments outoome are below: Pithreat mild risk) 04 P(threat moderate risk) 0.6 shr Upcoming is a festival in your city, and you have obtained a permit for a food stand. A thorization to check was obtained, the chemical composition was obtained, and the food served was deemed threatening. Now you want to make sure that this food does not pose a major risk to the event So, what is the probability that the food poses a major risk, given its been deemed threatening from your analysis? Homework Assignment 1 Spring 2019 (c) Assume two states Ai, A2 that are muly exclusive and span the whole statee with unknown probabilities P(A), PA). Based on historical information, you have found for some outcome O that: Using Bayes rule, what are the values for P(A), P(A2)? Answer:

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