A bank offers both adjustable-rate and fixed-rate mortgage loans on residential
ID: 3180146 • Letter: A
Question
A bank offers both adjustable-rate and fixed-rate mortgage loans on residential properties, which are classified into three categories: single-family houses, condominiums, and multifamily dwellings. The table contains the data collected from 3,750 loans that were selected. Single-Family Condo Multifamily Total Adjustable 1,500 788 337 2,625 Fixed-Rate 375 377 373 1,125 Total 1,875 1,165 710 3,750 a.) Find the probability that a randomly selected loan was an adjustable loan. b.) Find the probability that a randomly selected loan was for a condo. c.) Find the probability that a randomly selected loan was a fixed-rate and for a condo. d.) Find the probability that a randomly selected loan was a fixed-rate or for a condo. e.) Find the probability that a randomly selected loan was for a condo given that it was a fixed-rate. f.) Find the probability that a randomly selected loan was for an adjustable loan given it was for a single-family dwelling. g.) Are the events loan for a condo and a fixed-rate loan mutually exclusive? Why or why not? h.) Are the events the loan for a adjustable loan and loan for a single-family dwelling independent? Why or why not?
Explanation / Answer
from above
a) probability =2625/3750
b) probability =1165/3750
c)probability =377/3750
d)probability =(1125+788)/3750=1913/3750
e)probability =377/1125
f)probability =1500/1875
g)no as thre are some elements in there
h)No, as P(adjustable and single family)=1500/3750 which is not equal to P(adjustable)*P(single family)
single family condo multifamily total adjustable 1500 788 337 2625 fixed rate 375 377 373 1125 total 1875 1165 710 3750