Answer :
To solve the problem of finding the probability that a customer will be seated at a round table or by the window, we follow these steps:
1. Identify the Total Number of Tables:
- There are a total of 60 tables in the restaurant.
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 Round Tables by the Window:
- There are 6 round tables by the window.
5. Use the Formula for the Probability of the Union of Two Events:
- We need to find the probability of the union of two events: being either a round table or a table by the window.
- The formula for the probability of either event A or event B occurring is:
[tex]\[
P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)
\][/tex]
6. Apply the Numbers to the Formula:
- Let [tex]\( P(\text{Round}) = \frac{38}{60} \)[/tex] (probability of a round table)
- Let [tex]\( P(\text{Window}) = \frac{13}{60} \)[/tex] (probability of a table by the window)
- Let [tex]\( P(\text{Round and Window}) = \frac{6}{60} \)[/tex] (probability of a round table that is also by the window)
7. Calculate the Probability:
- [tex]\[
P(\text{Round or Window}) = \frac{38}{60} + \frac{13}{60} - \frac{6}{60} = \frac{45}{60}
\][/tex]
8. Simplify the Probability:
- The fraction [tex]\(\frac{45}{60}\)[/tex] simplifies to [tex]\(\frac{3}{4}\)[/tex].
Converting [tex]\(\frac{3}{4}\)[/tex] to a decimal gives 0.75, which matches with the provided answer.
Therefore, the probability that a customer will be seated at a round table or by the window is [tex]\(\frac{45}{60}\)[/tex].
The correct answer is C. [tex]\(\frac{45}{60}\)[/tex].
1. Identify the Total Number of Tables:
- There are a total of 60 tables in the restaurant.
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 Round Tables by the Window:
- There are 6 round tables by the window.
5. Use the Formula for the Probability of the Union of Two Events:
- We need to find the probability of the union of two events: being either a round table or a table by the window.
- The formula for the probability of either event A or event B occurring is:
[tex]\[
P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)
\][/tex]
6. Apply the Numbers to the Formula:
- Let [tex]\( P(\text{Round}) = \frac{38}{60} \)[/tex] (probability of a round table)
- Let [tex]\( P(\text{Window}) = \frac{13}{60} \)[/tex] (probability of a table by the window)
- Let [tex]\( P(\text{Round and Window}) = \frac{6}{60} \)[/tex] (probability of a round table that is also by the window)
7. Calculate the Probability:
- [tex]\[
P(\text{Round or Window}) = \frac{38}{60} + \frac{13}{60} - \frac{6}{60} = \frac{45}{60}
\][/tex]
8. Simplify the Probability:
- The fraction [tex]\(\frac{45}{60}\)[/tex] simplifies to [tex]\(\frac{3}{4}\)[/tex].
Converting [tex]\(\frac{3}{4}\)[/tex] to a decimal gives 0.75, which matches with the provided answer.
Therefore, the probability that a customer will be seated at a round table or by the window is [tex]\(\frac{45}{60}\)[/tex].
The correct answer is C. [tex]\(\frac{45}{60}\)[/tex].
