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Answer :
To solve the problem of finding the probability that a customer will be seated at a round table or by the window, we can use the principle of inclusion-exclusion. Here's how to approach it step-by-step:
1. Identify the total number of tables:
- The restaurant has 60 tables in total.
2. Determine the number of round tables:
- There are 38 round tables.
3. Determine the number of tables by the window:
- There are 13 tables located by the window.
4. Determine the number of round tables by the window:
- There are 6 round tables that are also located by the window.
5. Use the principle of inclusion-exclusion:
To find the probability of a table being either round or by the window, we need to consider overlapping tables (round tables by the window) to avoid counting them twice.
- Add the number of round tables and the number of window tables:
[tex]\(38 + 13 = 51\)[/tex]
- Subtract the number of round tables by the window since they have been counted twice:
[tex]\(51 - 6 = 45\)[/tex]
6. Calculate the probability:
- The probability is the number of favorable outcomes (tables that are either round or by the window) divided by the total number of tables.
- So, the probability is [tex]\(\frac{45}{60}\)[/tex].
Therefore, the answer is A. [tex]\(\frac{45}{60}\)[/tex] which represents the probability that a customer will be seated at a round table or by the window.
1. Identify the total number of tables:
- The restaurant has 60 tables in total.
2. Determine the number of round tables:
- There are 38 round tables.
3. Determine the number of tables by the window:
- There are 13 tables located by the window.
4. Determine the number of round tables by the window:
- There are 6 round tables that are also located by the window.
5. Use the principle of inclusion-exclusion:
To find the probability of a table being either round or by the window, we need to consider overlapping tables (round tables by the window) to avoid counting them twice.
- Add the number of round tables and the number of window tables:
[tex]\(38 + 13 = 51\)[/tex]
- Subtract the number of round tables by the window since they have been counted twice:
[tex]\(51 - 6 = 45\)[/tex]
6. Calculate the probability:
- The probability is the number of favorable outcomes (tables that are either round or by the window) divided by the total number of tables.
- So, the probability is [tex]\(\frac{45}{60}\)[/tex].
Therefore, the answer is A. [tex]\(\frac{45}{60}\)[/tex] which represents the probability that a customer will be seated at a round table or by the window.
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