Approximately 85% of persons age 70 to 84 live in their own household and are income-qualified for home purchases.

If four persons are randomly selected from this population, the probability that exactly two of the four live in their own household and are income-qualified is:

a. 0.8916

b. 0.4182

c. 0.0975

d. 0.0138

e. 0.5404

The probability that exactly two of the four live in their own household and are income-qualified is  = .0975

Step-by-step explanation:

Given -

Approximately 85% of persons age 70 to 84 live in their own household and are income-qualified for home purchases.

Probability of sucess ( p ) = 85% =.85

Probability of failure ( q ) = 1 - .85 =.15

n = 4

From combination of n events taking r sucess we use binomial distribution

where , r = 2

the probability that exactly two of the four live in their own household and are income-qualified is =

                =

                 =

                 = .0975