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Answer :
We are given that there are $60$ tables in total, with $38$ round tables and $13$ tables by the window. Among these, $6$ 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 states that the total count of tables with at least one desired property is given by
$$
\text{Number of tables} = \text{(round tables)} + \text{(window tables)} - \text{(tables that are both)}
$$
Substituting the given values, we have
$$
\text{Number of tables} = 38 + 13 - 6 = 45.
$$
Next, the probability that a randomly seated customer will be placed at a table that is either round or by the window is
$$
\text{Probability} = \frac{45}{60}.
$$
Thus, the correct answer is
$$
\frac{45}{60},
$$
which corresponds to option B.
To find the number of tables that are either round or by the window, we use the inclusion-exclusion principle. This states that the total count of tables with at least one desired property is given by
$$
\text{Number of tables} = \text{(round tables)} + \text{(window tables)} - \text{(tables that are both)}
$$
Substituting the given values, we have
$$
\text{Number of tables} = 38 + 13 - 6 = 45.
$$
Next, the probability that a randomly seated customer will be placed at a table that is either round or by the window is
$$
\text{Probability} = \frac{45}{60}.
$$
Thus, the correct answer is
$$
\frac{45}{60},
$$
which corresponds to option B.
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