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?

To solve the problems, we will use basic probability principles: A. The probability that a respondent owned a home is calculated by dividing the number of respondents who answered "Yes" by the total number of respondents: \( P(\text{Owns Home}) = \frac{1249}{2082} \approx 0.6003 \) or 60.03%. B. The probability that a respondent in the \( 18-34 \) age group owned a home is found by dividing the number of "Yes" responses in that age group by the total number of respondents in that group: \( P(\text{Owns Home | 18-34}) = \frac{117}{450} \approx 0.26 \) or 26%. C. The probability that a respondent did not own a home can be calculated as: \( P(\text{Does Not Own Home}) = 1 - P(\text{Owns Home}) = 1 - 0.6003 \approx 0.3997 \) or 39.97%. D. The probability that a respondent in the \( 18-34 \) age group did not own a home is: \( P(\text{Does Not Own Home | 18-34}) = 1 - P(\text{Owns Home | 18-34}) = 1 - 0.26 \approx 0.74 \) or 74%.