You are working for a bank and your supervisor asked you to predict the default risk for cach of the risk categories. The risk categories are coded A or B and are developed based on historical loan records. You construct the table below to summarize your assessment of the joint probabilities of customer risk categories (A or B) and the outcome (Pay back or default). Outcome Pay Back 0.52 0.36 Default Signal A 0.04 B 0.08 (3) What is the probability of risk category A given these joint probabilities? (Show your calculation) What is the probubility that a customer "default" given her risk is categorized in A? (Show your calculation) (3) What is the probubility that a customer "pay back" given her risk is categorized in B? (Show your calculation) (3)

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