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 the problem and find the probability that a customer will be seated at a round table or by the window, we can use the principle of inclusion-exclusion. Here's a step-by-step solution:

1. Identify Total Numbers:
- Total tables in the restaurant: 60
- Round tables: 38
- Tables by the window: 13
- Round tables by the window: 6

2. Find the Probability of Round or Window Table:
- We want the probability of a table being either round or by the window, but we must be careful not to double-count the tables that are both round and by the window.

3. Apply the Inclusion-Exclusion Principle:
- First, add the number of round tables and the number of tables by the window:
- Round tables + Window tables = 38 + 13 = 51
- Subtract the tables that are double-counted (round and by the window):
- Total round or window tables = 51 - 6 = 45

4. Calculate the Probability:
- The probability that a customer will be seated at a round table or by the window is the number of round or window tables divided by the total number of tables.
- Probability = Favorable outcomes / Total outcomes = 45 / 60 = 0.75

5. Conclusion:
- The probability that a customer will be seated at a round table or by the window is [tex]$\frac{45}{60}$[/tex], which simplifies to [tex]$\frac{3}{4}$[/tex].
- Thus, the correct answer is [tex]$\frac{45}{60}$[/tex], corresponding to option C.