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Answer :
To solve the problem, we need to find the probability that a customer will be seated at either a round table or by the window. We can use the principle of Inclusion-Exclusion for this.
Step 1: Define the groups.
- Total number of tables: 60
- Number of round tables: 38
- Number of tables by the window: 13
- Number of round tables by the window (overlap): 6
Step 2: Apply the Inclusion-Exclusion Principle.
The probability that a customer will be seated at either a round table or by the window is given by:
[tex]\[ P(\text{Round or Window}) = P(\text{Round}) + P(\text{Window}) - P(\text{Round and Window}) \][/tex]
Step 3: Calculate each probability.
- Probability of a round table: [tex]\(\frac{38}{60}\)[/tex]
- Probability of a table by the window: [tex]\(\frac{13}{60}\)[/tex]
- Probability of a round table by the window (overlap): [tex]\(\frac{6}{60}\)[/tex]
Step 4: Insert the values into the formula.
[tex]\[ P(\text{Round or Window}) = \frac{38}{60} + \frac{13}{60} - \frac{6}{60} \][/tex]
Step 5: Simplify the expression.
Combine the fractions:
[tex]\[ P(\text{Round or Window}) = \frac{38 + 13 - 6}{60} = \frac{45}{60} \][/tex]
Thus, the probability that a customer will be seated at a round table or by the window is [tex]\(\frac{45}{60}\)[/tex].
The correct answer is B. [tex]\(\frac{45}{60}\)[/tex].
Step 1: Define the groups.
- Total number of tables: 60
- Number of round tables: 38
- Number of tables by the window: 13
- Number of round tables by the window (overlap): 6
Step 2: Apply the Inclusion-Exclusion Principle.
The probability that a customer will be seated at either a round table or by the window is given by:
[tex]\[ P(\text{Round or Window}) = P(\text{Round}) + P(\text{Window}) - P(\text{Round and Window}) \][/tex]
Step 3: Calculate each probability.
- Probability of a round table: [tex]\(\frac{38}{60}\)[/tex]
- Probability of a table by the window: [tex]\(\frac{13}{60}\)[/tex]
- Probability of a round table by the window (overlap): [tex]\(\frac{6}{60}\)[/tex]
Step 4: Insert the values into the formula.
[tex]\[ P(\text{Round or Window}) = \frac{38}{60} + \frac{13}{60} - \frac{6}{60} \][/tex]
Step 5: Simplify the expression.
Combine the fractions:
[tex]\[ P(\text{Round or Window}) = \frac{38 + 13 - 6}{60} = \frac{45}{60} \][/tex]
Thus, the probability that a customer will be seated at a round table or by the window is [tex]\(\frac{45}{60}\)[/tex].
The correct answer is B. [tex]\(\frac{45}{60}\)[/tex].
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