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Answer :
To solve the problem, we're trying to find the probability that a randomly selected table is either round or located by the window at the restaurant.
Here's how we can approach this:
1. Determine the Total Number of Tables:
The restaurant has a total of 60 tables.
2. Count the Round Tables:
There are 38 round tables.
3. Count the Tables by the Window:
There are 13 tables located by the window.
4. Count the Tables that are Both Round and by the Window:
There are 6 tables that are both round and located by the window.
5. Calculate the Number of Tables that are Either Round or by the Window:
To avoid double-counting the tables that are both round and by the window, we use the formula for the union of two sets in probability:
[tex]\[
\text{Tables either round or by the window} = (\text{Round tables}) + (\text{Window tables}) - (\text{Tables that are both round and by the window})
\][/tex]
Plugging in the numbers:
[tex]\[
38 + 13 - 6 = 45
\][/tex]
6. Calculate the Probability:
The probability that a randomly selected table is either round or located by the window is the number of favorable outcomes (tables that are either round or by the window) divided by the total number of tables:
[tex]\[
\text{Probability} = \frac{\text{Tables either round or by the window}}{\text{Total tables}} = \frac{45}{60}
\][/tex]
7. Simplify the Probability:
Simplifying the fraction [tex]\(\frac{45}{60}\)[/tex], we find that:
[tex]\[
\frac{45}{60} = \frac{3}{4}
\][/tex]
So, the probability is [tex]\( \frac{3}{4} \)[/tex], or 0.75.
Therefore, the correct answer is D. [tex]\(\frac{45}{60}\)[/tex], which simplifies to 0.75 or 75%.
Here's how we can approach this:
1. Determine the Total Number of Tables:
The restaurant has a total of 60 tables.
2. Count the Round Tables:
There are 38 round tables.
3. Count the Tables by the Window:
There are 13 tables located by the window.
4. Count the Tables that are Both Round and by the Window:
There are 6 tables that are both round and located by the window.
5. Calculate the Number of Tables that are Either Round or by the Window:
To avoid double-counting the tables that are both round and by the window, we use the formula for the union of two sets in probability:
[tex]\[
\text{Tables either round or by the window} = (\text{Round tables}) + (\text{Window tables}) - (\text{Tables that are both round and by the window})
\][/tex]
Plugging in the numbers:
[tex]\[
38 + 13 - 6 = 45
\][/tex]
6. Calculate the Probability:
The probability that a randomly selected table is either round or located by the window is the number of favorable outcomes (tables that are either round or by the window) divided by the total number of tables:
[tex]\[
\text{Probability} = \frac{\text{Tables either round or by the window}}{\text{Total tables}} = \frac{45}{60}
\][/tex]
7. Simplify the Probability:
Simplifying the fraction [tex]\(\frac{45}{60}\)[/tex], we find that:
[tex]\[
\frac{45}{60} = \frac{3}{4}
\][/tex]
So, the probability is [tex]\( \frac{3}{4} \)[/tex], or 0.75.
Therefore, the correct answer is D. [tex]\(\frac{45}{60}\)[/tex], which simplifies to 0.75 or 75%.
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