Alright, let's work through this question step by step.
1. Identify Total Number of Places:
From the table, there are 7 places listed.
2. Count the Number of Cities:
The places which are cities (marked with V) from the table are:
- Rome
- Tokyo
- Houston
- Miami
- Toronto
Thus, the total number of cities is 5.
3. Calculate Probability of Chosen Place Being a City:
The probability \( P(A) \) that a randomly chosen place is a city is given by:
[tex]\[
P(A) = \frac{\text{Number of cities}}{\text{Total number of places}} = \frac{5}{7}
\][/tex]
4. Calculate Probability of Complement Event (Not a City):
The complementary event \( A^C \) is the event that the chosen place is not a city. The probability \( P(A^C) \) can be calculated as:
[tex]\[
P(A^C) = 1 - P(A)
\][/tex]
Therefore:
[tex]\[
P(A^C) = 1 - \frac{5}{7} = \frac{7}{7} - \frac{5}{7} = \frac{2}{7}
\][/tex]
So, the probability \( P(A^C) \), which is the probability that the chosen place is not a city, is \(\frac{2}{7}\).
Therefore, the correct answer is:
C. [tex]\(\frac{2}{7}\)[/tex].
