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Answer :
We start by noting the following information:
- 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 total number of tables that are either round or by the window, we use the inclusion-exclusion principle, which states:
[tex]$$
\text{Number of round or window tables} = \text{Round} + \text{Window} - \text{Both}.
$$[/tex]
Substituting the given numbers:
[tex]$$
\text{Number of round or window tables} = 38 + 13 - 6 = 45.
$$[/tex]
Next, the probability that a customer will be seated at a table that is either round or by the window is given by the ratio of the favorable outcomes (tables that are round or by the window) over the total number of tables:
[tex]$$
\text{Probability} = \frac{45}{60}.
$$[/tex]
Thus, the correct answer is:
[tex]$$
\frac{45}{60}.
$$[/tex]>
This corresponds to option B.
- 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 total number of tables that are either round or by the window, we use the inclusion-exclusion principle, which states:
[tex]$$
\text{Number of round or window tables} = \text{Round} + \text{Window} - \text{Both}.
$$[/tex]
Substituting the given numbers:
[tex]$$
\text{Number of round or window tables} = 38 + 13 - 6 = 45.
$$[/tex]
Next, the probability that a customer will be seated at a table that is either round or by the window is given by the ratio of the favorable outcomes (tables that are round or by the window) over the total number of tables:
[tex]$$
\text{Probability} = \frac{45}{60}.
$$[/tex]
Thus, the correct answer is:
[tex]$$
\frac{45}{60}.
$$[/tex]>
This corresponds to option B.
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