To determine the probability \( P(A^C) \), where \( A \) is the event that a place is a city, we first need to identify all the places that are not cities and then calculate their probability.
Let's start by examining the provided table:
[tex]\[
\begin{tabular}{|c|c|c|}
\hline
Place & Is a city & Is in North America \\
\hline
Rome & [tex]$\times$[/tex] & \\
\hline
Tokyo & [tex]$\checkmark$[/tex] & \\
\hline
Houston & [tex]$\checkmark$[/tex] & [tex]$\checkmark$[/tex] \\
\hline
Peru & [tex]$\times$[/tex] & \\
\hline
Miami & [tex]$\checkmark$[/tex] & [tex]$\checkmark$[/tex] \\
\hline
Toronto & [tex]$\checkmark$[/tex] & [tex]$\checkmark$[/tex] \\
\hline
Canada & [tex]$\times$[/tex] & [tex]$\checkmark$[/tex] \\
\hline
\end{tabular}
\][/tex]
We are given that \( A \) represents the event that a place is a city. Therefore, \( A^C \) represents the event that a place is not a city.
From the table:
- The total number of places is \( 7 \).
- The places that are not cities are:
- Rome
- Peru
- Canada
There are \( 3 \) places that are not cities (Rome, Peru, and Canada).
The probability \( P(A^C) \) is calculated as:
[tex]\[
P(A^C) = \frac{\text{Number of places that are not cities}}{\text{Total number of places}} = \frac{3}{7}
\][/tex]
Thus, the answer is:
[tex]\[ \boxed{\frac{3}{7}} \][/tex]
Therefore, the correct answer is:
B. [tex]\( \frac{3}{7} \)[/tex]
