Question

in a local high school, there are 244 seniors. of those seniors, 108 are enrolled in ap english, 148 are enrolled in ap calculus, and 76 are enrolled in both ap english and ap calculus. create a venn diagram to represent this situation and use it to answer the questions below.
how many students are taking neither ap english nor ap calculus? 64 students
how many students are taking ap english but not ap calculus? 32 students
how many students are taking ap english or ap calculus? 180 students
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question 32
a survey asks: which online services have you used in the last month:

• twitter
• facebook
• have used both

the results show 21% of those surveyed have used twitter, 83% have used facebook, and 12% have used both.
what percent of the people surveyed used neither twitter nor facebook? %
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Explanation:

Step1: Use the principle of inclusion - exclusion

The formula for \(n(A\cup B)=n(A)+n(B)-n(A\cap B)\). Here, let \(A\) be the set of people who used Twitter (\(n(A) = 21\%\)) and \(B\) be the set of people who used Facebook (\(n(B)=83\%\)), and \(n(A\cap B) = 12\%\).
So, \(n(A\cup B)=21\%+83\%-12\%\).

Step2: Calculate \(n(A\cup B)\)

\(n(A\cup B)=21 + 83-12=92\%\).

Step3: Find the percentage of people who used neither

The total percentage is \(100\%\). Let \(x\) be the percentage of people who used neither. Then \(x = 100\%-n(A\cup B)\).
Substitute \(n(A\cup B) = 92\%\) into the formula: \(x=100 - 92\).

Answer:

\(8\%\)