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Answer :
To solve this problem, we want to find the probability that a customer will be seated at a table that is either round or by the window. We can use the principle of inclusion-exclusion to find this probability.
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 Tables that are Round:
There are 38 round tables.
3. Identify the Number of Tables Located by the Window:
There are 13 tables by the window.
4. Identify the Number of Tables that are Both Round and by the Window:
There are 6 tables that are both round and by the window.
5. Use the Principle of Inclusion-Exclusion:
To avoid double-counting the tables that are both round and by the window, we apply the inclusion-exclusion principle:
[tex]\[
\text{Number of tables that are round or by the window} = (\text{number of round tables}) + (\text{number of window tables}) - (\text{number of tables that are both round and by the window})
\][/tex]
Plug in the values:
[tex]\[
= 38 + 13 - 6 = 45
\][/tex]
6. Calculate the Probability:
The probability that a customer will be seated at a table that is either round or by the window is the number of such tables divided by the total number of tables:
[tex]\[
\text{Probability} = \frac{45}{60}
\][/tex]
7. Simplify the Fraction:
Simplify [tex]\(\frac{45}{60}\)[/tex] by dividing both the numerator and the denominator by their greatest common divisor, which is 15:
[tex]\[
\frac{45}{60} = \frac{3}{4} = 0.75
\][/tex]
Hence, the probability that a customer will be seated at a round table or by the window is 0.75. Therefore, 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 Tables that are Round:
There are 38 round tables.
3. Identify the Number of Tables Located by the Window:
There are 13 tables by the window.
4. Identify the Number of Tables that are Both Round and by the Window:
There are 6 tables that are both round and by the window.
5. Use the Principle of Inclusion-Exclusion:
To avoid double-counting the tables that are both round and by the window, we apply the inclusion-exclusion principle:
[tex]\[
\text{Number of tables that are round or by the window} = (\text{number of round tables}) + (\text{number of window tables}) - (\text{number of tables that are both round and by the window})
\][/tex]
Plug in the values:
[tex]\[
= 38 + 13 - 6 = 45
\][/tex]
6. Calculate the Probability:
The probability that a customer will be seated at a table that is either round or by the window is the number of such tables divided by the total number of tables:
[tex]\[
\text{Probability} = \frac{45}{60}
\][/tex]
7. Simplify the Fraction:
Simplify [tex]\(\frac{45}{60}\)[/tex] by dividing both the numerator and the denominator by their greatest common divisor, which is 15:
[tex]\[
\frac{45}{60} = \frac{3}{4} = 0.75
\][/tex]
Hence, the probability that a customer will be seated at a round table or by the window is 0.75. Therefore, the correct answer is:
C. [tex]\(\frac{45}{60}\)[/tex]
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