Answer :
We are given:
- Total number of tables:
[tex]$$T = 60$$[/tex]
- Number of round tables:
[tex]$$R = 38$$[/tex]
- Number of tables located by the window:
[tex]$$W = 13$$[/tex]
- Number of round tables by the window (overlap):
[tex]$$R \cap W = 6$$[/tex]
We need to find the probability that a randomly assigned table is either a round table or a table by the window. To do so, we first determine the total number of tables that are either round or by the window using the principle of inclusion and exclusion.
The number of tables that are either round or by the window is given by:
[tex]$$|R \cup W| = R + W - |R \cap W|$$[/tex]
Substitute the given values:
[tex]$$|R \cup W| = 38 + 13 - 6 = 45$$[/tex]
Now, the probability that a customer will be seated at a table that is either round or by the window is:
[tex]$$P = \frac{|R \cup W|}{T} = \frac{45}{60}$$[/tex]
Thus, the correct answer is:
[tex]$$\frac{45}{60}$$[/tex]
This corresponds to option C.
- Total number of tables:
[tex]$$T = 60$$[/tex]
- Number of round tables:
[tex]$$R = 38$$[/tex]
- Number of tables located by the window:
[tex]$$W = 13$$[/tex]
- Number of round tables by the window (overlap):
[tex]$$R \cap W = 6$$[/tex]
We need to find the probability that a randomly assigned table is either a round table or a table by the window. To do so, we first determine the total number of tables that are either round or by the window using the principle of inclusion and exclusion.
The number of tables that are either round or by the window is given by:
[tex]$$|R \cup W| = R + W - |R \cap W|$$[/tex]
Substitute the given values:
[tex]$$|R \cup W| = 38 + 13 - 6 = 45$$[/tex]
Now, the probability that a customer will be seated at a table that is either round or by the window is:
[tex]$$P = \frac{|R \cup W|}{T} = \frac{45}{60}$$[/tex]
Thus, the correct answer is:
[tex]$$\frac{45}{60}$$[/tex]
This corresponds to option C.
