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{45}{60}[/tex]
D. [tex]\frac{47}{60}[/tex]

To find the probability that a customer will be seated at a round table or by the window, we can use the principle of inclusion and exclusion. This principle allows us to account for tables that are both round and by the window, so they're not counted twice.

Here’s a step-by-step breakdown:

1. Identify Total Tables: There are a total of 60 tables in the restaurant.

2. Count Round Tables: Out of these, 38 tables are round.

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

4. Count Overlapping Tables: Among these, 6 tables are both round and by the window.

5. Apply Inclusion-Exclusion Principle:
To find the number of tables that are either round or by the window, add the number of round tables and the number of window tables, then subtract the number of tables that are counted twice (both round and by the window).

Calculation:
[tex]\[
\text{Number of tables} = (\text{Round tables}) + (\text{Window tables}) - (\text{Round and Window tables})
\][/tex]
[tex]\[
= 38 + 13 - 6 = 45
\][/tex]

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

[tex]\[
\text{Probability} = \frac{45}{60}
\][/tex]

7. Simplify the Fraction:
Simplifying [tex]$\frac{45}{60}$[/tex] gives [tex]$\frac{3}{4}$[/tex] or 0.75.

So, the correct answer is [tex]$ \frac{45}{60} $[/tex] or 0.75, which corresponds to option C.