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  3. 5 probability relationships aa aa a mortgage is a loan...

Question: 5 probability relationships aa aa a mortgage is a loan...

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5. Probability relationships Aa Aa A mortgage is a loan that the borrower uses to finance the purchase of a home. There are two basic types of mortgage loans: the fixed-rate mortgage and the adjustable-rate mortgage (ARM). For the purposes of this problem, assume that all mortgages are either fixed-rate or adjustable-rate Apart from the classification of a mortgage as fixed-rate or adjustable-rate, conventional mortgage loans (loans that are not government-insured) are categorized as prime or subprime. A subprime mortgage is made to a borrower who is perceived as a high credit risk. For the purposes of this problem, assume that all conventional mortgages are either prime or subprime Note: For the rest of this problem, the term mortgage refers to a loan that is not government-insured (a conventional mortgage) Consider this experiment: A mortgage is randomly selected and categorized as prime or subprime and as fixed-rate or adjustable-rate A the event that the mortgage has an adjustable rate F the event that the mortgage has a fixed rate P = the event that the mortgage is prime the event that the mortgage is subprime S Now consider events S and F. Which of the following Venn diagrams most accurately shows how events S and F are related to the sample space? Event S Event F Event S Event F Event S Event F Diagram 1 Diagram 2 Diagram 3 O Diagram 1 Diagram Diagram 3 Are events S and F mutually exclusive? O No Q YesAre events S and F complementary? O Yes O No The Mortgage Bankers Association conducted a survey of more than 45 million mortgage loans and found the following composition of outstanding mortgages: Percent of Mortgages* 70% 16% 7% 7% Mortgage Characteristics Prime, fixed-rate Prime, adjustable-rate Subprime, fixed-rate Subprime, adjustable-rate Source: Mortgage Bankers Association, National Delinquency Survey, December 6, 2007. Mortgages refers to the conventional (non-FHA, non-VA) mortgages in the survey Continue to consider the experiment of randomly selecting a mortgage and categorizing it as prime or subprime and as fixed-rate or adjustable-rate What is the probability that a randomly selected mortgage is either subprime or fixed-rate (or both)?

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