College

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

Answer :

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

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.

3. Identify the number of tables by the window:
There are 13 tables located by the window.

4. Identify the number of tables that are both round and by the window:
There are 6 tables that are both round and by the window.

5. Calculate the number of tables that are either round or by the window using the principle of inclusion-exclusion:
[tex]\[ \text{Number of round or window tables} = (\text{round tables}) + (\text{window tables}) - (\text{round and window tables}) \][/tex]

[tex]\[ = 38 + 13 - 6 = 45 \][/tex]

6. Determine the probability that a customer will be seated at a table that is either round or by the window:
[tex]\[ \text{Probability} = \frac{\text{Number of round or window tables}}{\text{Total number of tables}} \][/tex]
[tex]\[ = \frac{45}{60} \][/tex]

Upon simplifying [tex]\(\frac{45}{60}\)[/tex], we get [tex]\(\frac{3}{4}\)[/tex] or [tex]\(0.75\)[/tex].

So, the correct probability is [tex]\( \frac{45}{60} \)[/tex], which corresponds to option D.