To determine the probability that a customer will be seated at a round table or by the window, we need to follow these steps:
1. Identify the Given Values:
- Total number of tables: 60
- Total number of round tables: 38
- Total number of window tables: 13
- Number of round tables that are also by the window: 6
2. Calculate the Number of Tables that are Either Round or By the Window:
We can use the principle of inclusion-exclusion to find this value. The formula to calculate the number of tables that are either round or by the window:
[tex]\[
\text{Round or Window} = \text{Number of Round Tables} + \text{Number of Window Tables} - \text{Number of Round Tables by the Window}
\][/tex]
Substituting the given values:
[tex]\[
\text{Round or Window} = 38 + 13 - 6 = 45
\][/tex]
3. Calculate the Probability:
The probability [tex]\(P\)[/tex] that a randomly assigned table is either round or by the window is given by the ratio of the number of tables that are either round or by the window to the total number of tables:
[tex]\[
P = \frac{\text{Round or Window Tables}}{\text{Total Tables}}
\][/tex]
Substituting the numbers:
[tex]\[
P = \frac{45}{60}
\][/tex]
4. Simplify the Fraction:
[tex]\[
\frac{45}{60} = \frac{3}{4} = 0.75
\][/tex]
Thus, the correct answer is [tex]\( \frac{45}{60} \)[/tex] (option A).
Therefore, the probability that a customer will be seated at a round table or by the window is indeed [tex]\(\frac{45}{60}\)[/tex].
