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{45}{60}[/tex]
B. [tex]\frac{41}{65}[/tex]
C. [tex]\frac{29}{60}[/tex]
D. [tex]\frac{47}{60}[/tex]

Answer :

We are given:

- Total number of tables: [tex]$60$[/tex]
- Number of round tables: [tex]$38$[/tex]
- Number of tables by the window: [tex]$13$[/tex]
- Number of tables that are both round and by the window: [tex]$6$[/tex]

To find the number of tables that are either round or by the window, we use the inclusion-exclusion principle. This principle states that if we have two sets, the number of elements in their union is given by:

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

Substitute the numbers:

[tex]$$
\text{Eligible tables} = 38 + 13 - 6 = 45
$$[/tex]

Thus, there are [tex]$45$[/tex] tables that are either round or by the window.

To find the probability that a customer is seated at one of these tables, we divide the number of eligible tables by the total number of tables:

[tex]$$
\text{Probability} = \frac{45}{60} = 0.75
$$[/tex]

This corresponds to the option:

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