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]$\frac{47}{60}$[/tex]

B. [tex]$\frac{29}{80}$[/tex]

C. [tex]$\frac{45}{60}$[/tex]

D. [tex]$\frac{41}{60}$[/tex]

To find the probability that a customer will be seated at a table that is either round or by the window, we'll follow these steps:

1. Total number of tables: The restaurant has 60 tables in total.

2. Round tables: There are 38 round tables.

3. Window tables: There are 13 tables located by the window.

4. Round and window tables: There are 6 tables that are both round and by the window.

5. Using the principle of Inclusion-Exclusion: To find the total number of tables that are either round or by the window, we'll add the number of round tables to the number of window tables and subtract the number of tables that are counted twice (i.e., those tables that are both round and by the window).

[tex]\[
\text{Number of either round or window tables} = \text{Round tables} + \text{Window tables} - \text{Round and window tables}
\][/tex]

Plugging in our numbers:

[tex]\[
\text{Number of either round or window tables} = 38 + 13 - 6 = 45
\][/tex]

6. Calculate the probability: The probability that a customer will be seated at a round table or by the window is then the number of either round or window tables divided by the total number of tables.

[tex]\[
\text{Probability} = \frac{\text{Number of either round or window tables}}{\text{Total number of tables}} = \frac{45}{60}
\][/tex]

7. Simplify the fraction (if necessary):

[tex]\[
\frac{45}{60} = \frac{3}{4} = 0.75
\][/tex]

Therefore, the correct answer is:

C. [tex]$\frac{45}{60}$[/tex]