High School

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

Answer :

To find the probability that a customer will be seated at a round table or by the window, we can use the formula for the probability of the union of two events. This formula is:

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

where:
- [tex]\( A \)[/tex] is the event of being seated at a round table,
- [tex]\( B \)[/tex] is the event of being seated by the window.

Let's determine each part:

1. Total Tables: There are 60 tables in the restaurant.

2. Round Tables: There are 38 round tables.

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

4. Round Tables by the Window: There are 6 round tables by the window.

Now, we'll use the formula:

- Probability of being seated at a round table, [tex]\( P(A) \)[/tex]:
[tex]\[ P(A) = \frac{\text{Number of round tables}}{\text{Total number of tables}} = \frac{38}{60} \][/tex]

- Probability of being seated by the window, [tex]\( P(B) \)[/tex]:
[tex]\[ P(B) = \frac{\text{Number of window tables}}{\text{Total number of tables}} = \frac{13}{60} \][/tex]

- Probability of being seated at a round table and by the window, [tex]\( P(A \text{ and } B) \)[/tex]:
[tex]\[ P(A \text{ and } B) = \frac{\text{Number of round tables by the window}}{\text{Total number of tables}} = \frac{6}{60} \][/tex]

Substitute these probabilities into the formula:

[tex]\[ P(A \text{ or } B) = \frac{38}{60} + \frac{13}{60} - \frac{6}{60} \][/tex]

[tex]\[ P(A \text{ or } B) = \frac{38 + 13 - 6}{60} \][/tex]
[tex]\[ P(A \text{ or } B) = \frac{45}{60} \][/tex]

So, the probability that a customer will be seated at a round table or by the window is [tex]\(\frac{45}{60}\)[/tex].

Therefore, the correct answer is:

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