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

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

Here's a step-by-step breakdown:

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 in the restaurant.

3. Identify the Number of Tables by the Window:
There are 13 tables located by the window.

4. Identify the Overlap (Round Tables by the Window):
There are 6 round tables that are also by the window.

5. Apply the Principle of Inclusion-Exclusion:
The probability of a table being either round or by the window is calculated as follows:

- Add the number of round tables and the number of tables by the window:
[tex]$ 38 + 13 = 51 $[/tex]

- Subtract the number of tables that are both round and by the window (since they are counted twice in the step above):
[tex]$ 51 - 6 = 45 $[/tex]

6. Calculate the Probability:
The total number of favorable tables (either round or by the window) is 45. Divide this by the total number of tables to find the probability:
[tex]$ \frac{45}{60} = 0.75 $[/tex]

Therefore, the probability that a customer will be seated at a round table or by the window is [tex]$\frac{45}{60} = \frac{3}{4}$[/tex], and the correct answer is:
C. [tex]$\frac{45}{60}$[/tex]