Answer :
To find the probability that a customer will be seated at a round table or by the window, we can use the formula for the probability of the union of two events. This formula is:
[tex]\[ P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B) \][/tex]
where:
- [tex]\( A \)[/tex] is the event of being seated at a round table,
- [tex]\( B \)[/tex] is the event of being seated by the window.
Let's determine each part:
1. Total Tables: There are 60 tables in the restaurant.
2. Round Tables: There are 38 round tables.
3. Tables by the Window: There are 13 tables located by the window.
4. Round Tables by the Window: There are 6 round tables by the window.
Now, we'll use the formula:
- Probability of being seated at a round table, [tex]\( P(A) \)[/tex]:
[tex]\[ P(A) = \frac{\text{Number of round tables}}{\text{Total number of tables}} = \frac{38}{60} \][/tex]
- Probability of being seated by the window, [tex]\( P(B) \)[/tex]:
[tex]\[ P(B) = \frac{\text{Number of window tables}}{\text{Total number of tables}} = \frac{13}{60} \][/tex]
- Probability of being seated at a round table and by the window, [tex]\( P(A \text{ and } B) \)[/tex]:
[tex]\[ P(A \text{ and } B) = \frac{\text{Number of round tables by the window}}{\text{Total number of tables}} = \frac{6}{60} \][/tex]
Substitute these probabilities into the formula:
[tex]\[ P(A \text{ or } B) = \frac{38}{60} + \frac{13}{60} - \frac{6}{60} \][/tex]
[tex]\[ P(A \text{ or } B) = \frac{38 + 13 - 6}{60} \][/tex]
[tex]\[ P(A \text{ or } B) = \frac{45}{60} \][/tex]
So, 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:
A. [tex]\(\frac{45}{60}\)[/tex]
[tex]\[ P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B) \][/tex]
where:
- [tex]\( A \)[/tex] is the event of being seated at a round table,
- [tex]\( B \)[/tex] is the event of being seated by the window.
Let's determine each part:
1. Total Tables: There are 60 tables in the restaurant.
2. Round Tables: There are 38 round tables.
3. Tables by the Window: There are 13 tables located by the window.
4. Round Tables by the Window: There are 6 round tables by the window.
Now, we'll use the formula:
- Probability of being seated at a round table, [tex]\( P(A) \)[/tex]:
[tex]\[ P(A) = \frac{\text{Number of round tables}}{\text{Total number of tables}} = \frac{38}{60} \][/tex]
- Probability of being seated by the window, [tex]\( P(B) \)[/tex]:
[tex]\[ P(B) = \frac{\text{Number of window tables}}{\text{Total number of tables}} = \frac{13}{60} \][/tex]
- Probability of being seated at a round table and by the window, [tex]\( P(A \text{ and } B) \)[/tex]:
[tex]\[ P(A \text{ and } B) = \frac{\text{Number of round tables by the window}}{\text{Total number of tables}} = \frac{6}{60} \][/tex]
Substitute these probabilities into the formula:
[tex]\[ P(A \text{ or } B) = \frac{38}{60} + \frac{13}{60} - \frac{6}{60} \][/tex]
[tex]\[ P(A \text{ or } B) = \frac{38 + 13 - 6}{60} \][/tex]
[tex]\[ P(A \text{ or } B) = \frac{45}{60} \][/tex]
So, 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:
A. [tex]\(\frac{45}{60}\)[/tex]
