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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 you can figure it out:
1. Identify the Total Tables:
The restaurant has a total of 60 tables.
2. Identify the Specific Tables:
- There are 38 round tables.
- There are 13 tables located by the window.
- There are 6 tables that are both round and located by the window.
3. Apply the Principle of Inclusion-Exclusion:
To find the number of tables that are either round or located by the window, you can add the number of round tables and window tables, then subtract the tables that are both (since these were counted twice).
[tex]\[
\text{Tables that are either round or by the window} = 38 + 13 - 6 = 45
\][/tex]
4. 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]\[
\text{Probability} = \frac{45}{60} = \frac{3}{4} = 0.75
\][/tex]
Therefore, the probability is [tex]\(0.75\)[/tex], which means that there is a 75% chance that a customer will be seated at a table that is either round or by the window. So the correct answer is:
C. [tex]\(\frac{47}{60}\)[/tex]
1. Identify the Total Tables:
The restaurant has a total of 60 tables.
2. Identify the Specific Tables:
- There are 38 round tables.
- There are 13 tables located by the window.
- There are 6 tables that are both round and located by the window.
3. Apply the Principle of Inclusion-Exclusion:
To find the number of tables that are either round or located by the window, you can add the number of round tables and window tables, then subtract the tables that are both (since these were counted twice).
[tex]\[
\text{Tables that are either round or by the window} = 38 + 13 - 6 = 45
\][/tex]
4. 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]\[
\text{Probability} = \frac{45}{60} = \frac{3}{4} = 0.75
\][/tex]
Therefore, the probability is [tex]\(0.75\)[/tex], which means that there is a 75% chance that a customer will be seated at a table that is either round or by the window. So the correct answer is:
C. [tex]\(\frac{47}{60}\)[/tex]
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