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Answer :
To solve this problem, we need to determine the probability that a customer will be seated at a table that is either round or by the window.
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.
3. Identify the number of tables by the window:
There are 13 tables located 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. Calculate the number of tables that are either round or by the window using the principle of inclusion-exclusion:
[tex]\[ \text{Number of round or window tables} = (\text{round tables}) + (\text{window tables}) - (\text{round and window tables}) \][/tex]
[tex]\[ = 38 + 13 - 6 = 45 \][/tex]
6. Determine the probability that a customer will be seated at a table that is either round or by the window:
[tex]\[ \text{Probability} = \frac{\text{Number of round or window tables}}{\text{Total number of tables}} \][/tex]
[tex]\[ = \frac{45}{60} \][/tex]
Upon simplifying [tex]\(\frac{45}{60}\)[/tex], we get [tex]\(\frac{3}{4}\)[/tex] or [tex]\(0.75\)[/tex].
So, the correct probability is [tex]\( \frac{45}{60} \)[/tex], which corresponds to option D.
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.
3. Identify the number of tables by the window:
There are 13 tables located 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. Calculate the number of tables that are either round or by the window using the principle of inclusion-exclusion:
[tex]\[ \text{Number of round or window tables} = (\text{round tables}) + (\text{window tables}) - (\text{round and window tables}) \][/tex]
[tex]\[ = 38 + 13 - 6 = 45 \][/tex]
6. Determine the probability that a customer will be seated at a table that is either round or by the window:
[tex]\[ \text{Probability} = \frac{\text{Number of round or window tables}}{\text{Total number of tables}} \][/tex]
[tex]\[ = \frac{45}{60} \][/tex]
Upon simplifying [tex]\(\frac{45}{60}\)[/tex], we get [tex]\(\frac{3}{4}\)[/tex] or [tex]\(0.75\)[/tex].
So, the correct probability is [tex]\( \frac{45}{60} \)[/tex], which corresponds to option D.
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