To determine [tex]\( P(A^C) \)[/tex], we need to understand both event [tex]\( A \)[/tex] and its complement [tex]\( A^C \)[/tex].
1. Identify Event [tex]\( A \)[/tex]:
- Event [tex]\( A \)[/tex] is defined as the place chosen being a city.
2. Count the Total Number of Places:
- There are a total of 7 places listed in the table.
3. Identify the Places that are Cities:
- The places that are cities from the table are Tokyo, Houston, New York, and Tijuana. Thus, there are 4 cities.
4. Determine the Complement Event [tex]\( A^C \)[/tex]:
- The complement of the event [tex]\( A \)[/tex] (denoted as [tex]\( A^C \)[/tex]) is the event that the place chosen is not a city.
5. Count the Number of Non-City Places:
- Total places = 7
- Number of cities = 4
- Number of non-cities = Total places - Number of cities
- Number of non-cities = 7 - 4 = 3
6. Calculate the Probability [tex]\( P(A^C) \)[/tex]:
- Probability of [tex]\( A^C \)[/tex] is the ratio of non-city places to the total number of places.
- [tex]\( P(A^C) = \frac{\text{Number of non-cities}}{\text{Total number of places}} \)[/tex]
- [tex]\( P(A^C) = \frac{3}{7} \)[/tex]
Therefore, the probability that a randomly chosen place is not a city is [tex]\( \frac{3}{7} \)[/tex].
Converting the fraction to a decimal, we get [tex]\( \frac{3}{7} \approx 0.42857142857142855 \)[/tex].
So, the probability [tex]\( P(A^C) \)[/tex] is approximately 0.42857142857142855.
