Answer :
To solve the problem of finding the probability that a customer will be seated at either a round table or a table by the window, we can use the principle of inclusion-exclusion. Here’s a step-by-step explanation:
1. Identify the Total Number of Tables:
The restaurant has a total of 60 tables.
2. Identify Specific Types of Tables:
- There are 38 round tables.
- There are 13 tables located by the window.
- Out of these, 6 tables are both round and by the window.
3. Calculate the Number of Tables that are Either Round or by the Window:
- To find the total number of tables that are either round or by the window, we use the principle of inclusion-exclusion:
- Add the number of round tables (38) and window tables (13).
- Subtract the number of tables that are both round and by the window (6) to avoid double-counting.
- Thus, the calculation is 38 + 13 - 6 = 45.
4. Calculate the Probability:
- The probability that a customer is seated at a table that is either round or by the window is the number of such tables divided by the total number of tables.
- Therefore, the probability is 45 out of 60.
5. Express the Probability:
- Simplify the fraction [tex]\(\frac{45}{60}\)[/tex], which simplifies to [tex]\(\frac{3}{4}\)[/tex].
- In decimal form, [tex]\(\frac{3}{4} = 0.75\)[/tex].
Thus, the probability that a customer will be seated at a round table or by the window is [tex]\(\frac{45}{60}\)[/tex], which matches option A.
1. Identify the Total Number of Tables:
The restaurant has a total of 60 tables.
2. Identify Specific Types of Tables:
- There are 38 round tables.
- There are 13 tables located by the window.
- Out of these, 6 tables are both round and by the window.
3. Calculate the Number of Tables that are Either Round or by the Window:
- To find the total number of tables that are either round or by the window, we use the principle of inclusion-exclusion:
- Add the number of round tables (38) and window tables (13).
- Subtract the number of tables that are both round and by the window (6) to avoid double-counting.
- Thus, the calculation is 38 + 13 - 6 = 45.
4. Calculate the Probability:
- The probability that a customer is seated at a table that is either round or by the window is the number of such tables divided by the total number of tables.
- Therefore, the probability is 45 out of 60.
5. Express the Probability:
- Simplify the fraction [tex]\(\frac{45}{60}\)[/tex], which simplifies to [tex]\(\frac{3}{4}\)[/tex].
- In decimal form, [tex]\(\frac{3}{4} = 0.75\)[/tex].
Thus, the probability that a customer will be seated at a round table or by the window is [tex]\(\frac{45}{60}\)[/tex], which matches option A.
