Question 6 A survey asks: Which online services have you used in the last month: - Twitter - Facebook The results show \( 37 \% \) of those surveyed have used Twitter, 58\% have used Facebook, and 9\% have used both. What percent of the people surveyed used neither Twitter nor Facebook? Question Help: Video Submit Question

To find the percentage of people who used neither Twitter nor Facebook, we can use the principle of inclusion-exclusion. Let: - \( A \) be the set of people who used Twitter. - \( B \) be the set of people who used Facebook. From the survey results, we have: - \( P(A) = 37\% \) (percentage of people who used Twitter) - \( P(B) = 58\% \) (percentage of people who used Facebook) - \( P(A \cap B) = 9\% \) (percentage of people who used both Twitter and Facebook) We want to find the percentage of people who used either Twitter or Facebook, which is given by the formula: \[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \] Substituting the values we have: \[ P(A \cup B) = 37\% + 58\% - 9\% \] Calculating this: \[ P(A \cup B) = 37\% + 58\% - 9\% = 86\% \] Now, to find the percentage of people who used neither Twitter nor Facebook, we subtract the percentage of people who used either service from 100%: \[ P(\text{neither}) = 100\% - P(A \cup B) = 100\% - 86\% = 14\% \] Thus, the percentage of people surveyed who used neither Twitter nor Facebook is **14%**.