\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}

Let event [tex]$A$[/tex] = The place is a city.
Let event [tex]$B$[/tex] = The place is in North America.

What is [tex]$P(A$[/tex] and [tex]$B)$[/tex]?

A. [tex]$\frac{3}{7}$[/tex]



Answer :

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]