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Answer :
To solve the probability problem, we need to determine the probability that a customer will be seated at a round table or by the window.
We'll follow these steps:
1. Identify Total Tables:
- The total number of tables in the restaurant is 60.
2. Count Round Tables:
- There are 38 round tables.
3. Count Window Tables:
- There are 13 tables situated by the window.
4. Identify Overlap (Round and Window Tables):
- Among those tables, there are 6 that are both round and by the window.
5. Apply the Inclusion-Exclusion Principle:
- To find the number of tables that are either round or by the window, we use the formula:
[tex]\[
\text{Number of Round or Window Tables} = \text{Round Tables} + \text{Window Tables} - \text{Round and Window Tables}
\][/tex]
- Plug in the values:
[tex]\[
38 + 13 - 6 = 45
\][/tex]
6. Calculate the Probability:
- The probability that a customer gets a table that is either round or by the window is the ratio of the qualifying tables to the total number of tables:
[tex]\[
\text{Probability} = \frac{\text{Number of Round or Window Tables}}{\text{Total Tables}} = \frac{45}{60}
\][/tex]
7. Simplify the Probability:
- [tex]\(\frac{45}{60}\)[/tex] simplifies to [tex]\(\frac{3}{4}\)[/tex], which is equivalent to 0.75.
Based on this solution, the correct answer is:
A. [tex]\(\frac{45}{60}\)[/tex]
We'll follow these steps:
1. Identify Total Tables:
- The total number of tables in the restaurant is 60.
2. Count Round Tables:
- There are 38 round tables.
3. Count Window Tables:
- There are 13 tables situated by the window.
4. Identify Overlap (Round and Window Tables):
- Among those tables, there are 6 that are both round and by the window.
5. Apply the Inclusion-Exclusion Principle:
- To find the number of tables that are either round or by the window, we use the formula:
[tex]\[
\text{Number of Round or Window Tables} = \text{Round Tables} + \text{Window Tables} - \text{Round and Window Tables}
\][/tex]
- Plug in the values:
[tex]\[
38 + 13 - 6 = 45
\][/tex]
6. Calculate the Probability:
- The probability that a customer gets a table that is either round or by the window is the ratio of the qualifying tables to the total number of tables:
[tex]\[
\text{Probability} = \frac{\text{Number of Round or Window Tables}}{\text{Total Tables}} = \frac{45}{60}
\][/tex]
7. Simplify the Probability:
- [tex]\(\frac{45}{60}\)[/tex] simplifies to [tex]\(\frac{3}{4}\)[/tex], which is equivalent to 0.75.
Based on this solution, the correct answer is:
A. [tex]\(\frac{45}{60}\)[/tex]
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