12. Probabllty relationships A mortgage is a loan that the borrower uses to fina
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Question
12. Probabllty relationships A mortgage is a loan that the borrower uses to finance the assume that all mortgages are elther fixed-rate or adjustable-rate purchase of a home. There are two basic types of ns: the flixed-rate mortgage and the adjustable-rate mortgage (ARM). For the purposes of this problem, fication of a mortgage as fixed-rate or adjustable-rate, conventional mortgage loans (loans that t-Insured) are categorized as prime or subprime. A subprime mortgage is made to a borrower s perceived as a high credit risk. For the purposes of this problem, assume that all conventional mortgages are either prime or subprime. 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 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 Now consider events P and F. Which of the following Venn diagrams most accurately shows how events P a related to the sample space? Event p Event F Event PEvent F Event P Event F Diagram 1 Diagram 2 Diagram 3Explanation / Answer
Event P and F is represented by diagram 2
Event P and A are not mutually exclusive.
Event P and A are not Complementary as their sum is not equal to 1.
Pr(A loan is either prime or fixed rate) = Pr(Prime) + Pr(Fixed rate) - Pr(Prime and fixed rate both)
= (0.70 + 0.16) + (0.70 + 0.07) - 0.70 = 0.93
Pr(Delinquent) = 0.06 ; Pr(Adjustable - rate mortgages) = 0.10
Pr(adjustable rate loan) = 0.16 + 0.07= 0.23
Pr(D and A) = Pr(D l A) * Pr(A) = 0.10 * 0.23 = 0.023
so we can say that events are not independent in nature.
Pr(D and A) = Pr(D) * Pr(A)
Pr(D and A) = 0.10
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