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Answer: 33%
ExplanationC is correct. First, we identify and define the relevant probabilities: A is the presence of a secured home mortgage loan via agency B is the prevalence of millennial borrowers P(A) is the probability of borrower having an agency secure their home mortgage loan. In this case, it is 62% or 0.62. P(B) is the probability of being a millennial borrower. Here it is 32% or 0.32. P(A|B) is the probability of having an agency-secured home mortgage loan given a millennial status, which is what we want to calculate. P(B|A) is the probability of being a millennial given the existence/presence of an agency-secured home mortgage loan. Here it is 17% or 0.17. P(B) Thus, P(A/B) = [0.17 * 0.62] / 0.32 = 0.329 = 0.33 or 33%. A is incorrect. This is just P(B|A). B is incorrect. This is the result of P(A)*P(B) D is incorrect. This is the result when the formula is miscalculated as P(B)/P(A) = 0.32/0.62= 0.516.
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A risk analyst working at a home loan company is in the process of updating a table that profiles the risks associated with borrowers. This table is crucial for creating and assessing home loans. The analyst is particularly interested in understanding the impact of government-backed mortgage companies in the United States—specifically Fannie Mae, Freddie Mac, and Ginnie Mae—on a borrower's likelihood of defaulting on their home loan. The following data has been collected:
Given these statistics, determine the probability that a millennial borrower has a home loan that is secured by a government agency.
A
17%
B
20%
C
33%
D
52%