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Answer :
Let's solve this problem step by step.
1. Identify the Total Number of Tables:
The restaurant has 60 tables in total.
2. Determine the Number of Round Tables and Window Tables:
- Round tables: 38 tables
- Tables by the window: 13 tables
3. Identify the Overlap (Round Tables by the Window):
There are 6 tables that are both round and by the window.
4. Use the Principle of Inclusion-Exclusion:
To find the number of tables that are either round or by the window, we use the inclusion-exclusion principle.
[tex]\[
\text{Number of round or window tables} = (\text{Number of round tables}) + (\text{Number of window tables}) - (\text{Number of round tables by the window})
\][/tex]
Plugging in the numbers:
[tex]\[
= 38 + 13 - 6 = 45
\][/tex]
5. Calculate the Probability:
The probability that a customer will be seated at a round table or by the window is the number of favorable tables divided by the total number of tables.
[tex]\[
\text{Probability} = \frac{\text{Number of round or window tables}}{\text{Total number of tables}} = \frac{45}{60}
\][/tex]
6. Select the Correct Answer:
The probability in fraction form is [tex]\(\frac{45}{60}\)[/tex]. When simplified, this fraction represents 0.75, indicating that 75% of the customers will be seated at either a round table or a window table.
Thus, the correct answer is B. [tex]\(\frac{45}{60}\)[/tex].
1. Identify the Total Number of Tables:
The restaurant has 60 tables in total.
2. Determine the Number of Round Tables and Window Tables:
- Round tables: 38 tables
- Tables by the window: 13 tables
3. Identify the Overlap (Round Tables by the Window):
There are 6 tables that are both round and by the window.
4. Use the Principle of Inclusion-Exclusion:
To find the number of tables that are either round or by the window, we use the inclusion-exclusion principle.
[tex]\[
\text{Number of round or window tables} = (\text{Number of round tables}) + (\text{Number of window tables}) - (\text{Number of round tables by the window})
\][/tex]
Plugging in the numbers:
[tex]\[
= 38 + 13 - 6 = 45
\][/tex]
5. Calculate the Probability:
The probability that a customer will be seated at a round table or by the window is the number of favorable tables divided by the total number of tables.
[tex]\[
\text{Probability} = \frac{\text{Number of round or window tables}}{\text{Total number of tables}} = \frac{45}{60}
\][/tex]
6. Select the Correct Answer:
The probability in fraction form is [tex]\(\frac{45}{60}\)[/tex]. When simplified, this fraction represents 0.75, indicating that 75% of the customers will be seated at either a round table or a window table.
Thus, the correct answer is B. [tex]\(\frac{45}{60}\)[/tex].
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