The chief loan officer of La Crosse Home Mortgage Company summarized the housing

Question

The chief loan officer of La Crosse Home Mortgage Company summarized the housing loans extended by the company in 2017 according to type and term of the loan. Her list shows that 65% of the loans were fixed-rate mortgages (F), 25% were adjustable-rate mortgages (A), and 10% belong to some other category (O) (mostly second trust-deed loans and home equity loans). Of the fixed-rate mortgages, 75% were 30-year loans and 25% were 15-year loans; of the adjustable-rate mortgages, 40% were 30-year loans and 60% were 15-year loans; finally, of the other loans extended, 25% were 20-year loans, 60% were 10-year loans, and 15% were for a term of 5 years or less. What is the probability that a home loan extended by La Crosse is for a term of 15 years?

Explanation / Answer

P(Home loan extended by La Crosse is for a term of 15 years)

= P(15 years| F) * P(F) + P(15 years| A) * P(A) + P(15 years| O) * P(O)

= 0.25*0.65 + 0.60*0.25 + 0*0.10

= 0.3125

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