A mortgage holding company has found that 1% 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.D
We have P(def) = 0.01. P(not def) = 0.99. P(two late payments/def) = 0.90. P(two late payments/not def) = 0.45. Using Bayes formula: p(def/two late payments) =
(0.01*0.9)/(0.01*0.9 + 0.99*0.45) = 0.0198 = 0.020.