Question

a survey of a groups web habits for the past month obtained the following information.
41% visited facebook.
40% visited linkedin.
36% visited google.
21% visited facebook and linkedin.
15% visited facebook and google.
18% visited linkedin and google.
10% visited all three sites.
find the percentage that visited none of these three sites last month.

Explanation:

Step1: Recall the principle of inclusion - exclusion

Let \(F\) be the set of people who visited Facebook, \(L\) be the set of people who visited LinkedIn, and \(G\) be the set of people who visited Google. The formula for \(|F\cup L\cup G|\) is \(|F|+|L|+|G|-|F\cap L|-|F\cap G|-|L\cap G|+|F\cap L\cap G|\).

Step2: Substitute the given percentages

We have \(|F| = 41\%\), \(|L|=40\%\), \(|G| = 36\%\), \(|F\cap L|=21\%\), \(|F\cap G| = 15\%\), \(|L\cap G|=18\%\), and \(|F\cap L\cap G| = 10\%\).
\[

$$\begin{align*} |F\cup L\cup G|&=41 + 40+36- 21-15 - 18+10\\ &=83 \end{align*}$$

\]

Step3: Calculate the percentage of people who visited none

The total percentage of people is \(100\%\). The percentage of people who visited none of the sites is \(100-|F\cup L\cup G|\). So \(100 - 83=17\%\).

Answer:

17