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Answer :
We are given the following:
- Total number of tables: [tex]$60$[/tex]
- Number of round tables: [tex]$38$[/tex]
- Number of tables located by the window: [tex]$13$[/tex]
- Number of round tables by the window: [tex]$6$[/tex]
We want the probability that a customer is seated at a table that is either round or by the window.
First, we find the total 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 inclusion-exclusion principle:
[tex]$$
\text{Total eligible tables} = \text{round tables} + \text{window tables} - \text{round tables by the window}
$$[/tex]
Substitute the given numbers:
[tex]$$
\text{Total eligible tables} = 38 + 13 - 6 = 45
$$[/tex]
Now, the probability that a customer will be seated at one of these tables is the number of eligible tables divided by the total number of tables:
[tex]$$
\text{Probability} = \frac{45}{60} = 0.75
$$[/tex]
Thus, the correct answer is:
[tex]$$
\frac{45}{60}
$$[/tex]
- Total number of tables: [tex]$60$[/tex]
- Number of round tables: [tex]$38$[/tex]
- Number of tables located by the window: [tex]$13$[/tex]
- Number of round tables by the window: [tex]$6$[/tex]
We want the probability that a customer is seated at a table that is either round or by the window.
First, we find the total 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 inclusion-exclusion principle:
[tex]$$
\text{Total eligible tables} = \text{round tables} + \text{window tables} - \text{round tables by the window}
$$[/tex]
Substitute the given numbers:
[tex]$$
\text{Total eligible tables} = 38 + 13 - 6 = 45
$$[/tex]
Now, the probability that a customer will be seated at one of these tables is the number of eligible tables divided by the total number of tables:
[tex]$$
\text{Probability} = \frac{45}{60} = 0.75
$$[/tex]
Thus, the correct answer is:
[tex]$$
\frac{45}{60}
$$[/tex]
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