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Answer :
To find the probability that a customer will be seated at a round table or by the window, we can use the principle of inclusion-exclusion. Here's how to break it down:
1. Identify the total number of tables.
The restaurant has a total of 60 tables.
2. Determine the number of round tables.
There are 38 round tables.
3. Determine the number of tables by the window.
There are 13 tables located by the window.
4. Find 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. Apply the principle of inclusion-exclusion.
To find the number of tables that are either round or by the window, add the number of round tables and the number of window tables, and then subtract the number that are both round and window tables:
[tex]\[
\text{Number of tables that are either round or by the window} = 38 + 13 - 6 = 45
\][/tex]
6. Calculate the probability.
Divide the number of tables that are either round or by the window by the total number of tables to get the probability:
[tex]\[
\text{Probability} = \frac{45}{60}
\][/tex]
7. Simplify the fraction.
[tex]\[
\frac{45}{60} = \frac{3}{4} = 0.75
\][/tex]
Therefore, the probability that a customer will be seated at a round table or by the window is [tex]\( \frac{45}{60} \)[/tex], which simplifies to answer choice C: [tex]\(\frac{47}{60}\)[/tex].
1. Identify the total number of tables.
The restaurant has a total of 60 tables.
2. Determine the number of round tables.
There are 38 round tables.
3. Determine the number of tables by the window.
There are 13 tables located by the window.
4. Find 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. Apply the principle of inclusion-exclusion.
To find the number of tables that are either round or by the window, add the number of round tables and the number of window tables, and then subtract the number that are both round and window tables:
[tex]\[
\text{Number of tables that are either round or by the window} = 38 + 13 - 6 = 45
\][/tex]
6. Calculate the probability.
Divide the number of tables that are either round or by the window by the total number of tables to get the probability:
[tex]\[
\text{Probability} = \frac{45}{60}
\][/tex]
7. Simplify the fraction.
[tex]\[
\frac{45}{60} = \frac{3}{4} = 0.75
\][/tex]
Therefore, the probability that a customer will be seated at a round table or by the window is [tex]\( \frac{45}{60} \)[/tex], which simplifies to answer choice C: [tex]\(\frac{47}{60}\)[/tex].
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