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Answer :
We are given:
- Total number of tables: [tex]$60$[/tex]
- Number of round tables: [tex]$38$[/tex]
- Number of tables by the window: [tex]$13$[/tex]
- Number of tables that are both round and by the window: [tex]$6$[/tex]
To find the number of tables that are either round or by the window, we use the inclusion-exclusion principle. This principle states that if we have two sets, the number of elements in their union is given by:
[tex]$$
\text{(Round or Window tables)} = (\text{Round tables}) + (\text{Window tables}) - (\text{Round and Window tables})
$$[/tex]
Substitute the numbers:
[tex]$$
\text{Eligible tables} = 38 + 13 - 6 = 45
$$[/tex]
Thus, there are [tex]$45$[/tex] tables that are either round or by the window.
To find the probability that a customer is seated at one of these tables, we divide the number of eligible tables by the total number of tables:
[tex]$$
\text{Probability} = \frac{45}{60} = 0.75
$$[/tex]
This corresponds to the option:
A. [tex]$\frac{45}{60}$[/tex]
- Total number of tables: [tex]$60$[/tex]
- Number of round tables: [tex]$38$[/tex]
- Number of tables by the window: [tex]$13$[/tex]
- Number of tables that are both round and by the window: [tex]$6$[/tex]
To find the number of tables that are either round or by the window, we use the inclusion-exclusion principle. This principle states that if we have two sets, the number of elements in their union is given by:
[tex]$$
\text{(Round or Window tables)} = (\text{Round tables}) + (\text{Window tables}) - (\text{Round and Window tables})
$$[/tex]
Substitute the numbers:
[tex]$$
\text{Eligible tables} = 38 + 13 - 6 = 45
$$[/tex]
Thus, there are [tex]$45$[/tex] tables that are either round or by the window.
To find the probability that a customer is seated at one of these tables, we divide the number of eligible tables by the total number of tables:
[tex]$$
\text{Probability} = \frac{45}{60} = 0.75
$$[/tex]
This corresponds to the option:
A. [tex]$\frac{45}{60}$[/tex]
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