Answer
The following Venn diagram:
Work Step by Step
(a)
Hence, the Venn diagram consists of 3 circles and 8 regions.
(b)
A number of visitors enjoyed exactly one of these activities is:
\[\begin{align}
& n\left( \text{exactly one of these activity} \right)=n\left( \text{I} \right)+n\left( \text{V} \right)+n\left( \text{VII} \right) \\
& =42+116+105 \\
& =263
\end{align}\]
Hence, the of visitors enjoyed exactly one of these activities is 263.
(c)
A number of visitors enjoyed none of these activities is:
\[\begin{align}
& n\left( \text{none of these activity} \right)=n\left( \text{VIII} \right) \\
& =25
\end{align}\]
Hence, the of visitors enjoyed none of these activities is 25.
(d)
The number of visitors enjoyed at least two of these activities is:
\[\begin{align}
& n\left( \text{at least 2 activity} \right)=n\left( \text{II} \right)+n\left( \text{III} \right)+n\left( \text{IV} \right)+n\left( \text{VI} \right) \\
& =13+2+0+47 \\
& =62
\end{align}\]
Hence, the of visitors enjoyed at least two of these activities is 62.
(e)
A number of visitors enjoyed snowboarding and ice skating but not skiing is:
\[\begin{align}
& n\left( \text{snowboarding and ice skating but not skiing} \right)=n\left( \text{IV} \right) \\
& =0
\end{align}\]
Hence, the no. of visitors enjoyed snowboarding and ice skating but not skiing is 0.
(f)
A number of visitors enjoyed snowboarding or ice skating, but not skiing is:
\[\begin{align}
& n\left( \text{snowboarding or ice skating but not skiing} \right)=n\left( \text{I} \right)+n\left( \text{IV} \right)+n\left( \text{VII} \right) \\
& =42+0+105 \\
& =147
\end{align}\]
Hence, the no. of visitors enjoyed snowboarding or ice skating, but not skiing is 147.
(g)
A number of visitors enjoyed only skiing is:
\[\begin{align}
& n\left( \text{only skiing} \right)=n\left( \text{V} \right) \\
& =116
\end{align}\]
Hence, the of visitors enjoyed only skiing is 116.
