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 60% of the loans were fixed-rate mortgages (F), 30% were adjustable-rate mortgages (A), and 10% belong to some other category (0) (mostly second trust-deed loans and home equity loans). Of the fixed-rate mortgages, 80% were 30-year loans and 20% were 15-year loans; of the adjustable-rate mortgages, 35% were 30-year loans and 65% 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. (a) Draw a tree diagram representing these data. 30 15 30 10 20 O 15 30 10 20 ca5 15 30 O 0 20 ca5 15 30 15 30 O 10 20 a5 10 20 ca5 15 30 (b) What is the probability that a home loan extended by La Crosse has an adjustable rate and is for a term of 15 years? 21 (c) What is the probability that a home loan extended by La Crosse is for a term of 15 years? 36

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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 60% of the loans were fixed-rate
mortgages (F), 30% were adjustable-rate mortgages (A), and 10% belong to some other category (0) (mostly second trust-deed loans and home equity loans). Of the fixed-rate mortgages, 80% were 30-year loans and
20% were 15-year loans; of the adjustable-rate mortgages, 35% were 30-year loans and 65% 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.
(a) Draw a tree diagram representing these data.
15
30
15
30
10
20 <=5
O 15
30
10
20
<=5
15
30
20
<=5
15
30
15
30
O 10 20 a 5 10 20 <=5 15 30
(b) What is the probability that a home loan extended by La Crosse has an adjustable rate and is for a term of 15 years?
21
(c) What is the probability that a home loan extended by La Crosse is for a term of 15 years?
36
Transcribed Image Text: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 60% of the loans were fixed-rate mortgages (F), 30% were adjustable-rate mortgages (A), and 10% belong to some other category (0) (mostly second trust-deed loans and home equity loans). Of the fixed-rate mortgages, 80% were 30-year loans and 20% were 15-year loans; of the adjustable-rate mortgages, 35% were 30-year loans and 65% 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. (a) Draw a tree diagram representing these data. 15 30 15 30 10 20 <=5 O 15 30 10 20 <=5 15 30 20 <=5 15 30 15 30 O 10 20 a 5 10 20 <=5 15 30 (b) What is the probability that a home loan extended by La Crosse has an adjustable rate and is for a term of 15 years? 21 (c) What is the probability that a home loan extended by La Crosse is for a term of 15 years? 36
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