(10) A mortgage holding company has found that 2% of its mortgage holders defaul
ID: 3356039 • Letter: #
Question
(10) A mortgage holding company has found that 2% 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 joint probability that a mortgagee has two or more late monthly payments and does not default on the mortgage? What is the joint probability that a mortgagee has one or less late monthly payments and does not default on the mortgage?Explanation / Answer
Here, we have 2% of the mortgage holders that default on their mortgages and hence 98% do not default. Amongst them, 90% of those who default (2%) are late on atleast last two payments as against 45% in case of those who do not default (98%). Hence, the probabilities are as shown below: -
The probability that a mortgage has two or more late monthly payments and does not default is 0.45*0.98=0.441.
The probability that a mortgage has two or more late monthly payments and does not default is 0.55*0.98=0.539.
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