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Answer :
To find 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 how we can calculate it step-by-step:
1. Identify the Total Number of Tables:
The restaurant has a total of 60 tables.
2. Identify the Number of Round Tables:
There are 38 round tables in the restaurant.
3. Identify the Number of Tables by the Window:
There are 13 tables located by the window.
4. Identify the Overlap (Round Tables by the Window):
There are 6 round tables that are also located by the window.
5. Apply the Inclusion-Exclusion Principle:
To find the probability that a customer will sit at either a round table or a table by the window, we need to consider the overlap. We calculate as follows:
- Total for round tables or window tables:
[tex]\[
\text{Round tables} + \text{Window tables} - \text{Round tables by the window}
\][/tex]
Which is:
[tex]\[
38 + 13 - 6 = 45
\][/tex]
6. Calculate the Probability:
The probability is then the number of favorable outcomes (either round or window tables) divided by the total number of tables:
[tex]\[
\frac{45}{60}
\][/tex]
7. Simplify the Fraction if Necessary:
- Simplify [tex]\(\frac{45}{60}\)[/tex] to [tex]\(\frac{3}{4}\)[/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 simplifies to [tex]\(\frac{3}{4}\)[/tex], or in decimal form, 0.75.
Looking at the options provided:
- A. [tex]\(\frac{29}{60}\)[/tex]
- B. [tex]\(\frac{41}{60}\)[/tex]
- C. [tex]\(\frac{45}{60}\)[/tex]
- D. [tex]\(\frac{47}{60}\)[/tex]
The correct answer is C. [tex]\(\frac{45}{60}\)[/tex], which simplifies to [tex]\(\frac{3}{4}\)[/tex].
1. Identify the Total Number of Tables:
The restaurant has a total of 60 tables.
2. Identify the Number of Round Tables:
There are 38 round tables in the restaurant.
3. Identify the Number of Tables by the Window:
There are 13 tables located by the window.
4. Identify the Overlap (Round Tables by the Window):
There are 6 round tables that are also located by the window.
5. Apply the Inclusion-Exclusion Principle:
To find the probability that a customer will sit at either a round table or a table by the window, we need to consider the overlap. We calculate as follows:
- Total for round tables or window tables:
[tex]\[
\text{Round tables} + \text{Window tables} - \text{Round tables by the window}
\][/tex]
Which is:
[tex]\[
38 + 13 - 6 = 45
\][/tex]
6. Calculate the Probability:
The probability is then the number of favorable outcomes (either round or window tables) divided by the total number of tables:
[tex]\[
\frac{45}{60}
\][/tex]
7. Simplify the Fraction if Necessary:
- Simplify [tex]\(\frac{45}{60}\)[/tex] to [tex]\(\frac{3}{4}\)[/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 simplifies to [tex]\(\frac{3}{4}\)[/tex], or in decimal form, 0.75.
Looking at the options provided:
- A. [tex]\(\frac{29}{60}\)[/tex]
- B. [tex]\(\frac{41}{60}\)[/tex]
- C. [tex]\(\frac{45}{60}\)[/tex]
- D. [tex]\(\frac{47}{60}\)[/tex]
The correct answer is C. [tex]\(\frac{45}{60}\)[/tex], which simplifies to [tex]\(\frac{3}{4}\)[/tex].
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