Answer :
Certainly! Let's solve this step-by-step.
First, we know that the restaurant has a total of 60 tables. Out of these:
- 38 are round tables.
- 13 tables are located by the window.
- There are 6 tables that are both round and located by the window.
To find the number of tables that are either round or by the window, we can use the principle of inclusion and exclusion. This principle states that the number of elements in the union of two sets is equal to the sum of the number of elements in each set, minus the number of elements that are in both sets.
Mathematically, this can be expressed as:
[tex]\[
\text{Number of tables that are either round or by the window} = (\text{Number of round tables}) + (\text{Number of tables by the window}) - (\text{Number of round tables by the window})
\][/tex]
Plugging in the values we know:
[tex]\[
(\text{Number of round tables or by the window}) = 38 + 13 - 6 = 45
\][/tex]
Now that we know there are 45 tables that are either round or by the window, we can find the probability that a customer will be seated at one of these tables. Probability is given by the number of favorable outcomes divided by the total number of possible outcomes. In this case, the number of favorable outcomes is the number of tables that are either round or by the window, and the total number of possible outcomes is the total number of tables.
Thus, the probability is:
[tex]\[
\text{Probability} = \frac{\text{Number of tables that are either round or by the window}}{\text{Total number of tables}} = \frac{45}{60}
\][/tex]
To simplify the fraction:
[tex]\[
\frac{45}{60} = \frac{3}{4} = 0.75
\][/tex]
The fraction [tex]\(\frac{45}{60}\)[/tex] simplifies directly to 0.75, which corresponds to one of the answer choices.
Therefore, the correct answer is:
[tex]\[
\boxed{\frac{45}{60}}
\][/tex]
First, we know that the restaurant has a total of 60 tables. Out of these:
- 38 are round tables.
- 13 tables are located by the window.
- There are 6 tables that are both round and located by the window.
To find the number of tables that are either round or by the window, we can use the principle of inclusion and exclusion. This principle states that the number of elements in the union of two sets is equal to the sum of the number of elements in each set, minus the number of elements that are in both sets.
Mathematically, this can be expressed as:
[tex]\[
\text{Number of tables that are either round or by the window} = (\text{Number of round tables}) + (\text{Number of tables by the window}) - (\text{Number of round tables by the window})
\][/tex]
Plugging in the values we know:
[tex]\[
(\text{Number of round tables or by the window}) = 38 + 13 - 6 = 45
\][/tex]
Now that we know there are 45 tables that are either round or by the window, we can find the probability that a customer will be seated at one of these tables. Probability is given by the number of favorable outcomes divided by the total number of possible outcomes. In this case, the number of favorable outcomes is the number of tables that are either round or by the window, and the total number of possible outcomes is the total number of tables.
Thus, the probability is:
[tex]\[
\text{Probability} = \frac{\text{Number of tables that are either round or by the window}}{\text{Total number of tables}} = \frac{45}{60}
\][/tex]
To simplify the fraction:
[tex]\[
\frac{45}{60} = \frac{3}{4} = 0.75
\][/tex]
The fraction [tex]\(\frac{45}{60}\)[/tex] simplifies directly to 0.75, which corresponds to one of the answer choices.
Therefore, the correct answer is:
[tex]\[
\boxed{\frac{45}{60}}
\][/tex]
