To determine the probability [tex]\( P(A^C) \)[/tex], where [tex]\( A \)[/tex] is the event that a chosen place is a city, and [tex]\( A^C \)[/tex] represents the complement of [tex]\( A \)[/tex] (i.e., the event that a chosen place is not a city), we will follow these steps:
1. Identify the Total Number of Places:
We have a total of 7 places listed in the table:
- India
- Tokyo
- Chicago
- Peru
- Miami
- Canada
- Mexico
2. Count the Number of Places That Are Cities:
From the table, the places that are cities are:
- Tokyo
- Chicago
- Miami
Thus, there are 3 places that are cities.
3. Calculate the Number of Places That Are Not Cities:
The total number of places is 7, and the number of places that are cities is 3. Therefore, the number of places that are not cities is:
[tex]\[
7 - 3 = 4
\][/tex]
4. Determine the Probability [tex]\( P(A^C) \)[/tex]:
To find the probability [tex]\( P(A^C) \)[/tex], we need to determine the ratio of the number of places that are not cities to the total number of places. This ratio is:
[tex]\[
P(A^C) = \frac{\text{Number of places that are not cities}}{\text{Total number of places}} = \frac{4}{7}
\][/tex]
The probability [tex]\( P(A^C) \)[/tex] represents the likelihood that a randomly chosen place from the table is not a city.
Given the choices provided, the answer is:
A. 4
