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Answer :
To solve the problem of finding the probability that a customer will be seated at a round table or by the window, we can follow these steps:
1. Identify the Total Number of Tables:
- The restaurant has a total of 60 tables.
2. Identify the Number of Round Tables and Tables by the Window:
- There are 38 round tables.
- There are 13 tables by the window.
3. Identify the Intersection:
- There are 6 tables that are both round and by the window.
4. Apply the Inclusion-Exclusion Principle:
- We want to find the probability of a table being round or by the window. We use the formula for the probability of the union of two events:
[tex]\[
P(\text{Round or Window}) = P(\text{Round}) + P(\text{Window}) - P(\text{Round and Window})
\][/tex]
- Substituting the corresponding numbers:
- [tex]\( P(\text{Round}) = 38 \)[/tex]
- [tex]\( P(\text{Window}) = 13 \)[/tex]
- [tex]\( P(\text{Round and Window}) = 6 \)[/tex]
5. Calculate the Number of Favorable Outcomes:
- The number of tables that are either round or by the window is:
[tex]\[
38 + 13 - 6 = 45
\][/tex]
6. Calculate the Probability:
- The probability is the number of favorable outcomes divided by the total number of tables, which is:
[tex]\[
\frac{45}{60}
\][/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 [tex]\(\frac{3}{4}\)[/tex] or 0.75.
Thus, the correct answer is choice D: [tex]\(\frac{45}{60}\)[/tex].
1. Identify the Total Number of Tables:
- The restaurant has a total of 60 tables.
2. Identify the Number of Round Tables and Tables by the Window:
- There are 38 round tables.
- There are 13 tables by the window.
3. Identify the Intersection:
- There are 6 tables that are both round and by the window.
4. Apply the Inclusion-Exclusion Principle:
- We want to find the probability of a table being round or by the window. We use the formula for the probability of the union of two events:
[tex]\[
P(\text{Round or Window}) = P(\text{Round}) + P(\text{Window}) - P(\text{Round and Window})
\][/tex]
- Substituting the corresponding numbers:
- [tex]\( P(\text{Round}) = 38 \)[/tex]
- [tex]\( P(\text{Window}) = 13 \)[/tex]
- [tex]\( P(\text{Round and Window}) = 6 \)[/tex]
5. Calculate the Number of Favorable Outcomes:
- The number of tables that are either round or by the window is:
[tex]\[
38 + 13 - 6 = 45
\][/tex]
6. Calculate the Probability:
- The probability is the number of favorable outcomes divided by the total number of tables, which is:
[tex]\[
\frac{45}{60}
\][/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 [tex]\(\frac{3}{4}\)[/tex] or 0.75.
Thus, the correct answer is choice D: [tex]\(\frac{45}{60}\)[/tex].
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