Answer :
We start by noting the following:
- The total number of tables is [tex]$60$[/tex].
- There are [tex]$38$[/tex] round tables.
- There are [tex]$13$[/tex] tables by the window.
- Among these, [tex]$6$[/tex] tables are both round and by the window.
To find the number of tables that are either round or by the window, we use the inclusion-exclusion principle. This principle tells us that the total in the union is given by
[tex]$$
\text{Union} = \text{Round} + \text{Window} - \text{Both}.
$$[/tex]
Substituting the given numbers, we have
[tex]$$
\text{Union} = 38 + 13 - 6 = 45.
$$[/tex]
Thus, there are [tex]$45$[/tex] tables that are either round or located by the window.
Next, the probability that a customer will be seated at a table which is either round or by the window is the ratio of these favorable tables to the total number of tables:
[tex]$$
\text{Probability} = \frac{45}{60} = \frac{3}{4}.
$$[/tex]
Since the options are given in the form of [tex]$\frac{45}{60}$[/tex], the correct answer is
[tex]$$
\boxed{\frac{45}{60}}.
$$[/tex]
- The total number of tables is [tex]$60$[/tex].
- There are [tex]$38$[/tex] round tables.
- There are [tex]$13$[/tex] tables by the window.
- Among these, [tex]$6$[/tex] tables are both round and by the window.
To find the number of tables that are either round or by the window, we use the inclusion-exclusion principle. This principle tells us that the total in the union is given by
[tex]$$
\text{Union} = \text{Round} + \text{Window} - \text{Both}.
$$[/tex]
Substituting the given numbers, we have
[tex]$$
\text{Union} = 38 + 13 - 6 = 45.
$$[/tex]
Thus, there are [tex]$45$[/tex] tables that are either round or located by the window.
Next, the probability that a customer will be seated at a table which is either round or by the window is the ratio of these favorable tables to the total number of tables:
[tex]$$
\text{Probability} = \frac{45}{60} = \frac{3}{4}.
$$[/tex]
Since the options are given in the form of [tex]$\frac{45}{60}$[/tex], the correct answer is
[tex]$$
\boxed{\frac{45}{60}}.
$$[/tex]