7. A survey asked 2082 adults if they owned a home. A total of 1249 survey respondents answered Yes. Of the 450 respondents in the \( 18-34 \) age groups, 117 responded Yes. Required: A. What is the probability that a respondent to the poll owned a home? B. What is the probability that a respondent in the \( 18-34 \) age group owned a home? C. What is the probability that a respondent to the poll did not own a home? D. What is the probability that a respondent in the \( 18-34 \) age group did not own a home?

Let's analyze each part of the problem step by step. ### Given Data: - **Total respondents:** 2,082 - **Total "Yes" responses (owned a home):** 1,249 - **Respondents in the 18-34 age group:** 450 - **"Yes" responses in the 18-34 age group:** 117 --- ### **A. Probability that a respondent to the poll owned a home** **Calculation:** \[ \text{Probability} = \frac{\text{Number of "Yes" responses}}{\text{Total number of respondents}} = \frac{1249}{2082} \] **Numerical Calculation:** \[ \frac{1249}{2082} \approx 0.599 \text{ or } 59.9\% \] **Answer:** The probability is approximately **59.9%**. --- ### **B. Probability that a respondent in the \( 18-34 \) age group owned a home** **Calculation:** \[ \text{Probability} = \frac{\text{Number of "Yes" responses in 18-34}}{\text{Total respondents in 18-34 age group}} = \frac{117}{450} \] **Numerical Calculation:** \[ \frac{117}{450} = 0.26 \text{ or } 26.0\% \] **Answer:** The probability is **26.0%**. --- ### **C. Probability that a respondent to the poll did not own a home** **Calculation:** \[ \text{Probability} = 1 - \text{Probability of owning a home} = 1 - \frac{1249}{2082} \] \[ = \frac{2082 - 1249}{2082} = \frac{833}{2082} \] **Numerical Calculation:** \[ \frac{833}{2082} \approx 0.3995 \text{ or } 40.0\% \] **Answer:** The probability is approximately **40.0%**. --- ### **D. Probability that a respondent in the \( 18-34 \) age group did not own a home** **Calculation:** \[ \text{Probability} = 1 - \text{Probability of owning a home in 18-34} = 1 - \frac{117}{450} \] \[ = \frac{450 - 117}{450} = \frac{333}{450} \] **Numerical Calculation:** \[ \frac{333}{450} = 0.74 \text{ or } 74.0\% \] **Answer:** The probability is **74.0%**. --- ### **Summary of Probabilities:** - **A.** 59.9% - **B.** 26.0% - **C.** 40.0% - **D.** 74.0%