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Answer :
To solve this problem, we need to determine the probability that a customer will be seated at either a round table or a table by the window. Here's how to do it step by step:
1. Identify Total Tables: The restaurant has a total of 60 tables.
2. Identify Round Tables: There are 38 round tables.
3. Identify Tables by the Window: There are 13 tables located by the window.
4. Identify Overlap (Round and by the Window): There are 6 tables that are both round and located by the window.
5. Use the Inclusion-Exclusion Principle: To find the total number of tables that are either round or by the window, use the formula:
[tex]\[
\text{Tables that are either round or by the window} = (\text{Round Tables}) + (\text{Window Tables}) - (\text{Round and Window Tables})
\][/tex]
Substitute the given values:
[tex]\[
= 38 + 13 - 6 = 45
\][/tex]
6. Calculate the Probability: The probability that a customer will be seated at a round table or by the window is the number of favorable tables divided by the total number of tables.
[tex]\[
\text{Probability} = \frac{45}{60}
\][/tex]
7. Simplify if Necessary: The fraction [tex]\(\frac{45}{60}\)[/tex] simplifies to [tex]\(\frac{3}{4}\)[/tex], but since the options provide [tex]\(\frac{45}{60}\)[/tex], we use it as it is to match the choices given.
Therefore, the correct answer is option A: [tex]\(\frac{45}{60}\)[/tex].
1. Identify Total Tables: The restaurant has a total of 60 tables.
2. Identify Round Tables: There are 38 round tables.
3. Identify Tables by the Window: There are 13 tables located by the window.
4. Identify Overlap (Round and by the Window): There are 6 tables that are both round and located by the window.
5. Use the Inclusion-Exclusion Principle: To find the total number of tables that are either round or by the window, use the formula:
[tex]\[
\text{Tables that are either round or by the window} = (\text{Round Tables}) + (\text{Window Tables}) - (\text{Round and Window Tables})
\][/tex]
Substitute the given values:
[tex]\[
= 38 + 13 - 6 = 45
\][/tex]
6. Calculate the Probability: The probability that a customer will be seated at a round table or by the window is the number of favorable tables divided by the total number of tables.
[tex]\[
\text{Probability} = \frac{45}{60}
\][/tex]
7. Simplify if Necessary: The fraction [tex]\(\frac{45}{60}\)[/tex] simplifies to [tex]\(\frac{3}{4}\)[/tex], but since the options provide [tex]\(\frac{45}{60}\)[/tex], we use it as it is to match the choices given.
Therefore, the correct answer is option A: [tex]\(\frac{45}{60}\)[/tex].
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