Question

A large lending institution issues both adjustable-rate and fixed-rate mortgage loans on residential property, which it classifies into three categories: single-family houses, condominiums, and multi-family dwellings. The following table displays probabilities based on the bank’s long-run lending behavior:

Mortgage Choices
	Single-Family	Condo	Multi-Family
Adjustable-Rate	_____ ?	.21	.09
Fixed-Rate	.1	.09	.11

What is the probability that a randomly selected customer will have a loan with an adjustable-rate or for a multi-family dwelling? Round your answer to 2 decimal places.

Answer 1

A large lending institution issues both adjustable rate and fixed rate mortgage loans on residential property , which it classifies into 3 categories

single family house

condominiums

and multi family dwellings

Mortgage choices	Single family	Condo	Multi family	total
Adjustable Rate	0.40	0.21	0.09	0.70
Fixed Rate	0.10	0.09	0.11	0.30
Total	0.50	0.30	0.20	1

Probability that a randomly selected customer will have a loan with an adjustable rate or for a multi family dwelling

= P( Adjustable rate or Multi Family)

= P( Adjustable rate ) +P( Multi Family )- P(Adjustable Rate and Multi Family)

= 0.70+0.20-0.09

= 0.81

Probability that a randomly selected customer = 0.81