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Answer :
To solve this problem, we need to find the probability that a customer will be seated at either a round table or a table by the window.
Here's how you can determine that probability:
1. Identify the Total Number of Tables: The restaurant has a total of 60 tables.
2. Count of Round Tables: There are 38 round tables.
3. Count of Tables by the Window: There are 13 tables by the window.
4. Count of Round Tables by the Window: There are 6 round tables that are also by the window. This number is important because these tables have been counted in both the round tables and the window tables categories.
5. Use the Inclusion-Exclusion Principle:
To avoid double-counting the round tables by the window, we apply the inclusion-exclusion principle, which tells us:
[tex]\[
\text{Total count of (round or window tables)} = (\text{Number of round tables}) + (\text{Number of window tables}) - (\text{Number of round tables by the window})
\][/tex]
Plug in the numbers:
[tex]\[
\text{Total count of (round or window tables)} = 38 + 13 - 6 = 45
\][/tex]
6. Calculate the Probability:
The probability that a customer will be seated at a round table or a table by the window is the ratio of favorable outcomes (round or window tables) to the total outcomes (total tables):
[tex]\[
\text{Probability} = \frac{\text{Number of (round or window tables)}}{\text{Total number of tables}}
\][/tex]
[tex]\[
\text{Probability} = \frac{45}{60} = \frac{3}{4} = 0.75
\][/tex]
The correct answer is:
D. [tex]\(\frac{45}{60}\)[/tex]
Here's how you can determine that probability:
1. Identify the Total Number of Tables: The restaurant has a total of 60 tables.
2. Count of Round Tables: There are 38 round tables.
3. Count of Tables by the Window: There are 13 tables by the window.
4. Count of Round Tables by the Window: There are 6 round tables that are also by the window. This number is important because these tables have been counted in both the round tables and the window tables categories.
5. Use the Inclusion-Exclusion Principle:
To avoid double-counting the round tables by the window, we apply the inclusion-exclusion principle, which tells us:
[tex]\[
\text{Total count of (round or window tables)} = (\text{Number of round tables}) + (\text{Number of window tables}) - (\text{Number of round tables by the window})
\][/tex]
Plug in the numbers:
[tex]\[
\text{Total count of (round or window tables)} = 38 + 13 - 6 = 45
\][/tex]
6. Calculate the Probability:
The probability that a customer will be seated at a round table or a table by the window is the ratio of favorable outcomes (round or window tables) to the total outcomes (total tables):
[tex]\[
\text{Probability} = \frac{\text{Number of (round or window tables)}}{\text{Total number of tables}}
\][/tex]
[tex]\[
\text{Probability} = \frac{45}{60} = \frac{3}{4} = 0.75
\][/tex]
The correct answer is:
D. [tex]\(\frac{45}{60}\)[/tex]
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