Let's analyze the given question step by step to find the probability \( P(A \text{ and } B) \).
We are given the following table:
[tex]\[
\begin{tabular}{|c|c|c|}
\hline
Place & Is a city & Is in North America \\
\hline
India & & \\
\hline
Tokyo & [tex]$\checkmark$[/tex] & \\
\hline
Houston & [tex]$\checkmark$[/tex] & [tex]$\checkmark$[/tex] \\
\hline
Peru & & [tex]$\checkmark$[/tex] \\
\hline
New York & [tex]$\checkmark$[/tex] & [tex]$\checkmark$[/tex] \\
\hline
Tijuana & [tex]$\checkmark$[/tex] & [tex]$\checkmark$[/tex] \\
\hline
Canada & & \\
\hline
\end{tabular}
\][/tex]
### Step 1: Identify the Total Number of Places
Firstly, we count the total number of places listed in the table. They are:
1. India
2. Tokyo
3. Houston
4. Peru
5. New York
6. Tijuana
7. Canada
Thus, the total number of places is 7.
### Step 2: Identify Places that are Both Cities and in North America
Next, we need to identify which places satisfy both event \( A \) (the place is a city) and event \( B \) (the place is in North America). These places are:
- Houston
- New York
- Tijuana
Thus, there are 3 places that are both cities and in North America.
### Step 3: Calculate the Probability \( P(A \text{ and } B) \)
The probability \( P(A \text{ and } B) \) is the ratio of the number of places that are both cities and in North America to the total number of places.
[tex]\[
P(A \text{ and } B) = \frac{\text{Number of places that are both cities and in North America}}{\text{Total number of places}}
\][/tex]
Substituting the values, we get:
[tex]\[
P(A \text{ and } B) = \frac{3}{7} \approx 0.42857142857142855
\][/tex]
### Conclusion
Therefore, the probability \( P(A \text{ and } B) \) is approximately \( 0.42857142857142855 \), which is closest to the answer:
[tex]\(\boxed{\frac{3}{7}}\)[/tex]
