To find the probability [tex]\( P(A \text{ and } B) \)[/tex], we need to determine the proportion of places that satisfy both conditions: being a city and being in North America.
Let's break down the problem step by step:
1. Count the total number of places:
- By examining the table, we see there are 6 places listed (Tokyo, Houston, New York, Tijuana, and Canada).
2. Identify the places that are both a city and in North America:
- From the table, the places that meet both criteria (city and in North America) are Houston and Tijuana.
3. Count the number of places that satisfy both conditions:
- We have identified 2 places (Houston and Tijuana) that are both a city and in North America.
4. Calculate the probability:
- The probability [tex]\( P(A \text{ and } B) \)[/tex] is calculated as the ratio of the number of places that are both a city and in North America to the total number of places.
Thus, the probability [tex]\( P(A \text{ and } B) \)[/tex] is:
[tex]\[
P(A \text{ and } B) = \frac{\text{Number of places that are both a city and in North America}}{\text{Total number of places}} = \frac{2}{6} = 0.3333333333333333
\][/tex]
So, the probability [tex]\( P(A \text{ and } B) \)[/tex] is approximately [tex]\( 0.3333 \)[/tex] or [tex]\( \frac{1}{3} \)[/tex].
