Assignment 2.2 Score: \( 84.67 / 100 \) Answered: \( 17 / 20 \) Progress saved Done A survey asks: Which online services have you used in the last month: - Twitter Facebook The results show \( 36 \% \) of those surveyed have used Twitter, 58\% have used Facebook, and 12\% have used both. What percent of the people surveyed used neither Twitter nor Facebook? Question Help: 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: - \( P(A) = 36\% \) (percentage of people who used Twitter) - \( P(B) = 58\% \) (percentage of people who used Facebook) - \( P(A \cap B) = 12\% \) (percentage of people who used both Twitter and Facebook) Using the inclusion-exclusion principle, the percentage of people who used either Twitter or Facebook (or both) is given by: \[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \] Substituting the values: \[ P(A \cup B) = 36\% + 58\% - 12\% \] \[ P(A \cup B) = 82\% \] This means that \( 82\% \) of the people surveyed used either Twitter or Facebook (or both). To find the percentage of people who used neither service, we subtract the percentage of people who used either service from \( 100\% \): \[ P(\text{neither}) = 100\% - P(A \cup B) \] \[ P(\text{neither}) = 100\% - 82\% \] \[ P(\text{neither}) = 18\% \] Therefore, \( 18\% \) of the people surveyed used neither Twitter nor Facebook.