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. Suppose
each loan made in 2020 was classified according to type of mortgage and type of property, resulting in the
following table. Consider the chance experiment of selecting one of these 3,750 loans at random. (Round
your answers to three decimal places.)
Single-Family Condo Multifamily Total
Adjustable 1,575 788 337 2,700
Fixed Rate 300 404 346 1,050
Total 1,875 1,192 683 3,750
(a) What is the probability that the selected loan will be for an adjustable rate mortgage?
(b) What is the probability that the selected loan will be for a multifamily property?
(c) What is the probability that the selected loan will not be for a single-family property?
(d) What is the probability that the selected loan will be for a single-family property or a condo?
(e) What is the probability that the selected loan will be for a multifamily property or for an adjustable
rate loan?
(f) What is the probability that the selected loan will be a fixed rate loan for a condo?
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a) 0.72
b) 0.182
c) 0.5
d) 0.818
e) 0.812
f) 0.108
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(a) The probability that the selected loan will be for an adjustable rate mortgage is given by the ratio of the number of adjustable rate mortgages to the total number of loans:
Probability = Number of adjustable rate mortgages / Total number of loans
Probability = 2700 / 3750 = 0.720
(b) The probability that the selected loan will be for a multifamily property is given by the ratio of the number of multifamily loans to the total number of loans:
Probability = Number of multifamily loans / Total number of loans
Probability = 683 / 3750 ≈ 0.182
(c) The probability that the selected loan will not be for a single-family property is given by the ratio of the number of loans that are not for single-family properties to the total number of loans:
Probability = Number of loans not for single-family properties / Total number of loans
Probability = (788 + 337 + 300 + 404 + 346) / 3750 = 2175 / 3750 ≈ 0.58
(d) The probability that the selected loan will be for a single-family property or a condo is given by the sum of the probabilities of the individual events:
Probability = Probability of single-family property + Probability of condo
Probability = 1875 / 3750 + 1192 / 3750 = 3067 / 3750 ≈ 0.818
(e) The probability that the selected loan will be for a multifamily property or for an adjustable rate loan is given by the sum of the probabilities of the individual events:
Probability = Probability of multifamily property + Probability of adjustable rate loan
Probability = 683 / 3750 + 2700 / 3750 = 3383 / 3750 ≈ 0.902
(f) The probability that the selected loan will be a fixed rate loan for a condo is given by the ratio of the number of fixed rate loans for condos to the total number of loans:
Probability = Number of fixed rate loans for condos / Total number of loans
Probability = 404 / 3750 ≈ 0.108
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