To solve for [tex]\( P(A \text{ and } B) \)[/tex], we need to find the probability that a place is both a city and in North America.
1. Count the total number of places listed in the table:
- Rome
- Tokyo
- Houston
- Peru
- Miami
- Toronto
- Canada
This gives us a total of [tex]\( 7 \)[/tex] places.
2. Identify the number of places that are both cities and in North America:
- Toronto is the only place that is both a city and in North America.
Therefore, the number of places that are both cities and in North America is [tex]\( 1 \)[/tex].
3. Calculate the probability [tex]\( P(A \text{ and } B) \)[/tex]:
[tex]\( P(A \text{ and } B) \)[/tex] is the number of places that are both cities and in North America divided by the total number of places.
[tex]\[
P(A \text{ and } B) = \frac{1}{7}
\][/tex]
To summarize, the probability that a place is both a city and in North America is [tex]\( \frac{1}{7} \)[/tex] or approximately [tex]\( 0.14285714285714285 \)[/tex].
