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Answer :
To determine the probability that a customer will be seated at a round table or by the window, follow these steps:
1. Identify Total Tables:
The restaurant has a total of 60 tables.
2. Identify Round Tables and Window Tables:
- The number of round tables is 38.
- The number of tables by the window is 13.
3. Identify Overlap (Round Tables by the Window):
There are 6 tables that are both round and by the window.
4. Calculate the Number of Tables that are Either Round or by the Window:
Use the principle of inclusion and exclusion to avoid double-counting the tables that are both round and by the window.
[tex]\[
\text{Number of tables either round or by the window} = (\text{Number of round tables}) + (\text{Number of window tables}) - (\text{Number of round tables by the window})
\][/tex]
Plugging in the numbers:
[tex]\[
38 \, (\text{round tables}) + 13 \, (\text{window tables}) - 6 \, (\text{round tables by the window}) = 45
\][/tex]
5. Calculate the Probability:
The probability is the ratio of the number of tables that are either round or by the window to the total number of tables.
[tex]\[
\text{Probability} = \frac{\text{Number of tables either round or by the window}}{\text{Total number of tables}} = \frac{45}{60}
\][/tex]
6. Simplify the Fraction:
[tex]\[
\frac{45}{60} = \frac{3}{4} = 0.75
\][/tex]
Thus, the probability that a customer will be seated at a round table or by the window is:
[tex]\[
\boxed{\frac{45}{60}}
\][/tex]
In this problem, this fraction simplifies to one of the provided multiple-choice answers:
[tex]\[
C. \frac{45}{60}
\][/tex]
1. Identify Total Tables:
The restaurant has a total of 60 tables.
2. Identify Round Tables and Window Tables:
- The number of round tables is 38.
- The number of tables by the window is 13.
3. Identify Overlap (Round Tables by the Window):
There are 6 tables that are both round and by the window.
4. Calculate the Number of Tables that are Either Round or by the Window:
Use the principle of inclusion and exclusion to avoid double-counting the tables that are both round and by the window.
[tex]\[
\text{Number of tables either round or by the window} = (\text{Number of round tables}) + (\text{Number of window tables}) - (\text{Number of round tables by the window})
\][/tex]
Plugging in the numbers:
[tex]\[
38 \, (\text{round tables}) + 13 \, (\text{window tables}) - 6 \, (\text{round tables by the window}) = 45
\][/tex]
5. Calculate the Probability:
The probability is the ratio of the number of tables that are either round or by the window to the total number of tables.
[tex]\[
\text{Probability} = \frac{\text{Number of tables either round or by the window}}{\text{Total number of tables}} = \frac{45}{60}
\][/tex]
6. Simplify the Fraction:
[tex]\[
\frac{45}{60} = \frac{3}{4} = 0.75
\][/tex]
Thus, the probability that a customer will be seated at a round table or by the window is:
[tex]\[
\boxed{\frac{45}{60}}
\][/tex]
In this problem, this fraction simplifies to one of the provided multiple-choice answers:
[tex]\[
C. \frac{45}{60}
\][/tex]
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