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

Sure, let's solve this problem step-by-step.

First, we need to determine the probability that a customer will be seated at either a round table or a table by the window.

We are given the following information:
- Total tables: 60
- Round tables: 38
- Tables by the window: 13
- Round tables by the window: 6

We want to find the probability of a table being either round or by the window. For this, we can use the formula for the union of two events:

[tex]\[ P(\text{Round or Window}) = P(\text{Round}) + P(\text{Window}) - P(\text{Round and Window}) \][/tex]

Let's break it down:

1. Calculate the number of round tables and window tables, without double-counting the tables that are both:

- Tables that are round: 38
- Tables that are by the window: 13
- Tables that are both round and by the window: 6

So, we use the formula:

[tex]\[ \text{Total (Round or Window)} = \text{Round tables} + \text{Tables by the window} - \text{Tables that are both} \][/tex]

Substituting the values:

[tex]\[ \text{Total (Round or Window)} = 38 + 13 - 6 = 45 \][/tex]

2. Calculate the probability:

[tex]\[ P(\text{Round or Window}) = \frac{\text{Total (Round or Window)}}{\text{Total tables}} = \frac{45}{60} \][/tex]

Thus, the probability that a customer will be seated at a round table or by the window is:

[tex]\[ \frac{45}{60} \][/tex]

So, the correct answer is:

A. [tex]\(\frac{45}{60}\)[/tex]