To solve the problem of finding the probability [tex]\( P(A \text{ and } B) \)[/tex], let's follow a structured step-by-step approach based on the given table and events.
1. Identify total number of places:
- The total number of places listed in the table is 7 (India, Tokyo, Houston, Peru, New York, Tijuana, Canada).
2. Identify places that are cities and in North America (both conditions must be satisfied):
- From the table, we have two places that are categorized as cities: Tokyo, Houston, New York, Tijuana.
- Next, we need to check which of these cities are in North America. According to the table:
- Houston (is a city, is in North America)
- New York (is a city, is in North America)
3. Count places satisfying both A and B:
- From the observations above, only Houston and New York qualify as both cities and located in North America.
- Therefore, there are 2 places that satisfy both conditions.
4. Calculate the probability [tex]\( P(A \text{ and } B) \)[/tex]:
- The formula for probability is:
[tex]\[
P(A \text{ and } B) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}
\][/tex]
- Here, the number of favorable outcomes (places that are both cities and in North America) is 2, and the total number of possible outcomes (total places listed) is 7.
Substituting the numbers, we get:
[tex]\[
P(A \text{ and } B) = \frac{2}{7}
\][/tex]
Therefore, the answer is [tex]\( \frac{2}{7} \)[/tex].
So, the correct option is:
A. [tex]\(\frac{2}{7}\)[/tex]
