A mortgage holding company has found that 3% of its mortgage holders default on their mortgage and lose the property. Furthermore, 90% of those who default are late on at least two monthly payments over the life of their mortgage as compared to 45% of those who do not default.
What is the probability that a mortgagee with two or more late monthly payments will default on the mortgage and lose the property?
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A. B. C. D. E.B
We have P(def)=0.03. P(not def) = 0.97. P(two late payments/def) = 0.90. P(two late payments/not def) = 0.45. Using Bayes formula: p(def/two late payments) =
(0.03*0.9)/(0.03*0.9 + 0.97*0.45) = 0.058.
To solve this problem, let's break it down step by step:
Let's assume we have 1000 mortgage holders as a sample size.
According to the information given:
Now, let's find the probability that a mortgagee with two or more late monthly payments will default on the mortgage and lose the property.
Out of the mortgage holders who were late on at least two monthly payments (27 + 427.5 = 454.5), 27 mortgage holders defaulted.
Therefore, the probability that a mortgagee with two or more late monthly payments will default on the mortgage and lose the property is 27/454.5, which is approximately 0.059.
Among the given answer choices, the closest option to this probability is B. 0.058.
So the correct answer is B. 0.058.