A mortgage is a loan that the borrower uses to finance the purchase of a home. T

Question

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 adustable-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 P and A. Which of the following Venn diagrams most accurately shows how events P and A are related to the sample space? Event P Event A Event P Event A Event PEvent A Diagram1 Diagram 2 Diagram

Explanation / Answer

Events P and A are Option B Diagram 2.

Events A and F are mutually Exclusive. Yes

No. S ana A are not Complementary.

Q.1

Pr(Prime or Adjustable) = Pr(Prime) + Pr(Adjustable) - Pr(Prime - adjustable)

= (0.70 + 0.16) + (0.16 + 0.07) - 0.16

= 0.93 or 93%

Q.2 Here D is the event that mortgage is delinquent and S is the subprime so for these two events to be independent.

Pr(D l S) = Pr(D)

Pr(D l S) = 0.16

and Pr(D) = 0.06

so no these two events are not independent.

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