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:
[tex]\[ P(\text{Round or Window}) = P(\text{Round}) + P(\text{Window}) - P(\text{Round and Window}) \][/tex]
Here’s a step-by-step breakdown:
1. Identify the total number of tables: There are 60 tables in total.
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 located by the window: There are 6 round tables by the window.
5. Calculate the probability for round tables alone:
- Number of round tables = 38
6. Calculate the probability for tables by the window alone:
- Number of window tables = 13
7. Calculate the overlap (tables that are both round and by the window):
- There are 6 tables that are counted as both round and by the window.
8. Use the formula to get the probability:
- Add the number of round tables and the number of window tables, then subtract the overlap (to avoid double-counting those tables that are both).
- [tex]\[ 38 + 13 - 6 = 45 \][/tex]
9. Calculate the probability:
- The probability is [tex]\(\frac{45}{60}\)[/tex].
Therefore, the correct answer is:
A. [tex]\(\frac{45}{60}\)[/tex]
[tex]\[ P(\text{Round or Window}) = P(\text{Round}) + P(\text{Window}) - P(\text{Round and Window}) \][/tex]
Here’s a step-by-step breakdown:
1. Identify the total number of tables: There are 60 tables in total.
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 located by the window: There are 6 round tables by the window.
5. Calculate the probability for round tables alone:
- Number of round tables = 38
6. Calculate the probability for tables by the window alone:
- Number of window tables = 13
7. Calculate the overlap (tables that are both round and by the window):
- There are 6 tables that are counted as both round and by the window.
8. Use the formula to get the probability:
- Add the number of round tables and the number of window tables, then subtract the overlap (to avoid double-counting those tables that are both).
- [tex]\[ 38 + 13 - 6 = 45 \][/tex]
9. Calculate the probability:
- The probability is [tex]\(\frac{45}{60}\)[/tex].
Therefore, the correct answer is:
A. [tex]\(\frac{45}{60}\)[/tex]