To determine [tex]\( P(A \text{ and } B) \)[/tex], we need to identify the places that satisfy both conditions: being a city (event [tex]\( A \)[/tex]) and being located in North America (event [tex]\( B \)[/tex]).
Given the places and their attributes:
1. mousion: This entry has no information about being a city or being in North America, so it doesn't count towards either event.
2. Peru: This is not a city, so it doesn't satisfy event [tex]\( A \)[/tex].
3. Miami: This is a city ([tex]\(\checkmark\)[/tex]) in North America ([tex]\(\checkmark\)[/tex]).
4. Toronto: This is a city ([tex]\(\checkmark\)[/tex]) in North America ([tex]\(\checkmark\)[/tex]).
5. Canada: This is not a city, just a country name, so it doesn't satisfy event [tex]\( A \)[/tex].
Now, let's count the total number of places and the number of places that satisfy both conditions:
- Total number of places: There are 5 places listed.
- Number of places that are both cities and in North America (event [tex]\( A \)[/tex] and event [tex]\( B \)[/tex]): Miami and Toronto are the ones that fit both criteria, making 2 places.
To find [tex]\( P(A \text{ and } B) \)[/tex], we divide the number of places that satisfy both conditions by the total number of places:
[tex]\[
P(A \text{ and } B) = \frac{\text{Number of places that are both cities and in North America}}{\text{Total number of places}} = \frac{2}{7}
\][/tex]
Thus, the probability [tex]\( P(A \text{ and } B) \)[/tex] is:
A. [tex]\(\frac{2}{7}\)[/tex].
The correct answer is
[tex]\[
\boxed{\frac{2}{7}}
\][/tex]
