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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]
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]
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