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Answer :
To find the probability that a customer will be seated at a round table or by the window, we can use the inclusion-exclusion principle. Let's break down the problem step by step:
1. Identify the total number of tables:
- There are 60 tables in total.
2. Determine how many tables are round:
- There are 38 round tables.
3. Determine how many tables are by the window:
- There are 13 tables located by the window.
4. Identify the overlap (tables that are both round and by the window):
- There are 6 tables that are both round and by the window.
5. Apply the inclusion-exclusion principle:
- To find the total number of tables that are either round or by the window, we need to add the number of round tables and the number of window tables, then subtract the overlap (since we've counted those twice).
- So, the calculation is:
[tex]\[ \text{Tables that are round or by the window} = 38 + 13 - 6 = 45 \][/tex]
6. Calculate the probability:
- The probability of a customer being seated at either a round table or a table by the window is the number of favorable tables divided by the total number of tables.
- Therefore, the probability is:
[tex]\[ \frac{45}{60} \][/tex]
From the provided options, the correct answer that represents this probability is:
C. [tex]\(\frac{45}{60}\)[/tex]
1. Identify the total number of tables:
- There are 60 tables in total.
2. Determine how many tables are round:
- There are 38 round tables.
3. Determine how many tables are by the window:
- There are 13 tables located by the window.
4. Identify the overlap (tables that are both round and by the window):
- There are 6 tables that are both round and by the window.
5. Apply the inclusion-exclusion principle:
- To find the total number of tables that are either round or by the window, we need to add the number of round tables and the number of window tables, then subtract the overlap (since we've counted those twice).
- So, the calculation is:
[tex]\[ \text{Tables that are round or by the window} = 38 + 13 - 6 = 45 \][/tex]
6. Calculate the probability:
- The probability of a customer being seated at either a round table or a table by the window is the number of favorable tables divided by the total number of tables.
- Therefore, the probability is:
[tex]\[ \frac{45}{60} \][/tex]
From the provided options, the correct answer that represents this probability is:
C. [tex]\(\frac{45}{60}\)[/tex]
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