Answer :
To solve the problem of finding the probability that a customer will be seated at a round table or by the window, you 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 Window Tables:
- There are 38 round tables.
- There are 13 tables located by the window.
3. Identify the Number of Round Tables by the Window:
- There are 6 tables that are both round and by the window.
4. Use the Formula for Probability of A or B:
- The probability of being seated at a round table or a table by the window can be calculated using the formula:
[tex]\[
P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)
\][/tex]
- Here, [tex]\( P(A) \)[/tex] is the probability of sitting at a round table, [tex]\( P(B) \)[/tex] is the probability of sitting by the window, and [tex]\( P(A \text{ and } B) \)[/tex] is the probability of sitting at a round table by the window.
5. Substitute the Known Values:
- The number of tables that are either round (38) or by the window (13) includes the 6 tables that are counted twice because they are both round and by the window.
6. Perform the Calculation:
[tex]\[
P(\text{round or window}) = \frac{38 + 13 - 6}{60} = \frac{45}{60}
\][/tex]
7. Simplify the Fraction if Possible:
- Simplify [tex]\(\frac{45}{60}\)[/tex] if needed, but here it reflects the answer choices directly.
8. Conclusion:
- The probability that a customer will be seated at a round table or by the window is [tex]\(\frac{45}{60}\)[/tex].
Therefore, the correct answer is C. [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 Window Tables:
- There are 38 round tables.
- There are 13 tables located by the window.
3. Identify the Number of Round Tables by the Window:
- There are 6 tables that are both round and by the window.
4. Use the Formula for Probability of A or B:
- The probability of being seated at a round table or a table by the window can be calculated using the formula:
[tex]\[
P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)
\][/tex]
- Here, [tex]\( P(A) \)[/tex] is the probability of sitting at a round table, [tex]\( P(B) \)[/tex] is the probability of sitting by the window, and [tex]\( P(A \text{ and } B) \)[/tex] is the probability of sitting at a round table by the window.
5. Substitute the Known Values:
- The number of tables that are either round (38) or by the window (13) includes the 6 tables that are counted twice because they are both round and by the window.
6. Perform the Calculation:
[tex]\[
P(\text{round or window}) = \frac{38 + 13 - 6}{60} = \frac{45}{60}
\][/tex]
7. Simplify the Fraction if Possible:
- Simplify [tex]\(\frac{45}{60}\)[/tex] if needed, but here it reflects the answer choices directly.
8. Conclusion:
- The probability that a customer will be seated at a round table or by the window is [tex]\(\frac{45}{60}\)[/tex].
Therefore, the correct answer is C. [tex]\(\frac{45}{60}\)[/tex].
