Math

QuestionCalculate the probabilities for home ownership statuses:
a. Own: 27%27\% b. Rent: 48%48\% c. No mortgage: 48%+27%=75%48\% + 27\% = 75\%.

Studdy Solution

STEP 1

Assumptions1. The percentages given for home ownership statuses of loan applicants are Rent48%, Mortgage25%, Own27% . The percentages represent the proportion of the total population of loan applicants3. The categories are mutually exclusive, meaning an applicant can only belong to one category

STEP 2

To calculate the probability that a randomly selected applicant owns his/her home, we simply use the given percentage for the 'Own' category.
(Own)=OwnpercentageTotalpercentage(Own) = \frac{Own\, percentage}{Total\, percentage}

STEP 3

Plug in the given values for the 'Own' percentage and the total percentage to calculate the probability.
(Own)=27%100%(Own) = \frac{27\%}{100\%}

STEP 4

Calculate the probability that a randomly selected applicant owns his/her home.
(Own)=27%100%=0.27(Own) = \frac{27\%}{100\%} =0.27

STEP 5

To calculate the probability that a randomly selected applicant rents, we use the given percentage for the 'Rent' category.
(Rent)=RentpercentageTotalpercentage(Rent) = \frac{Rent\, percentage}{Total\, percentage}

STEP 6

Plug in the given values for the 'Rent' percentage and the total percentage to calculate the probability.
(Rent)=48%100%(Rent) = \frac{48\%}{100\%}

STEP 7

Calculate the probability that a randomly selected applicant rents.
(Rent)=48%100%=0.48(Rent) = \frac{48\%}{100\%} =0.48

STEP 8

To calculate the probability that a randomly selected applicant does not have a mortgage, we subtract the 'Mortgage' percentage from the total percentage.
(NotMortgage)=TotalpercentageMortgagepercentage(Not\, Mortgage) = Total\, percentage - Mortgage\, percentage

STEP 9

Plug in the given values for the 'Mortgage' percentage and the total percentage to calculate the probability.
(NotMortgage)=100%25%(Not\, Mortgage) =100\% -25\%

STEP 10

Calculate the probability that a randomly selected applicant does not have a mortgage.
(NotMortgage)=100%25%=75%=0.75(Not\, Mortgage) =100\% -25\% =75\% =0.75So, the probabilities are as followsa. The probability that a randomly selected applicant owns his/her home is0.27. b. The probability that a randomly selected applicant rents is0.48. c. The probability that a randomly selected applicant does not have a mortgage is0.75.

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