High School

Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ 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]

Answer :

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

Here's a step-by-step breakdown:

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 in the restaurant.

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

4. Identify the Overlap (Round Tables by the Window):
There are 6 round tables that are also by the window.

5. Apply the Principle of Inclusion-Exclusion:
The probability of a table being either round or by the window is calculated as follows:

- Add the number of round tables and the number of tables by the window:
[tex]\( 38 + 13 = 51 \)[/tex]

- Subtract the number of tables that are both round and by the window (since they are counted twice in the step above):
[tex]\( 51 - 6 = 45 \)[/tex]

6. Calculate the Probability:
The total number of favorable tables (either round or by the window) is 45. Divide this by the total number of tables to find the probability:
[tex]\( \frac{45}{60} = 0.75 \)[/tex]

Therefore, the probability that a customer will be seated at a round table or by the window is [tex]\(\frac{45}{60} = \frac{3}{4}\)[/tex], and the correct answer is:
C. [tex]\(\frac{45}{60}\)[/tex]