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------------------------------------------------ Select the correct answer.

A restaurant has a total of 60 tables. Of those tables, 38 are round, and 13 are located by the window. There are 6 round tables by the window. If tables are randomly assigned to customers, what is the probability that a customer will be seated at a round table or by the window?

A. [tex]\frac{41}{60}[/tex]
B. [tex]\frac{29}{60}[/tex]
C. [tex]\frac{47}{60}[/tex]
D. [tex]\frac{45}{60}[/tex]

To solve this problem, we need to determine the probability that a customer will be seated at a table that is either round or by the window.

1. Identify the total number of tables:
The restaurant has a total of 60 tables.

2. Identify the number of round tables:
There are 38 round tables.

3. Identify the number of tables by the window:
There are 13 tables located by the window.

4. Identify the number of tables that are both round and by the window:
There are 6 tables that are both round and by the window.

5. Calculate the number of tables that are either round or by the window using the principle of inclusion-exclusion:
[tex]\[ \text{Number of round or window tables} = (\text{round tables}) + (\text{window tables}) - (\text{round and window tables}) \][/tex]

[tex]\[ = 38 + 13 - 6 = 45 \][/tex]

6. Determine the probability that a customer will be seated at a table that is either round or by the window:
[tex]\[ \text{Probability} = \frac{\text{Number of round or window tables}}{\text{Total number of tables}} \][/tex]
[tex]\[ = \frac{45}{60} \][/tex]

Upon simplifying [tex]$\frac{45}{60}$[/tex], we get [tex]$\frac{3}{4}$[/tex] or [tex]$0.75$[/tex].

So, the correct probability is [tex]$ \frac{45}{60} $[/tex], which corresponds to option D.