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Answer :
To solve this problem, we need to determine the probability that a customer will be seated at a round table or by the window.
We have the following data:
- Total tables: 60
- Round tables: 38
- Tables by the window: 13
- Round tables by the window: 6
To find the probability of a customer being seated at a round table or by the window, we use the inclusion-exclusion principle. This principle helps us account for tables that are both round and by the window, which are counted twice if we simply add the number of round tables and window tables.
The formula to find the probability is:
[tex]\[
\text{Probability} = \frac{\text{Round tables} + \text{Window tables} - \text{Round tables by the Window}}{\text{Total tables}}
\][/tex]
Substitute the numbers into the formula:
[tex]\[
\text{Probability} = \frac{38 + 13 - 6}{60}
\][/tex]
Perform the arithmetic:
1. Add the round and window tables: [tex]\(38 + 13 = 51\)[/tex]
2. Subtract the round tables by the window: [tex]\(51 - 6 = 45\)[/tex]
So, the expression becomes:
[tex]\[
\frac{45}{60}
\][/tex]
When simplified, this fraction is equivalent to:
[tex]\[
\frac{3}{4} = 0.75
\][/tex]
Thus, the probability that a customer will be seated at a round table or by the window is 0.75. Looking at the answer choices, this probability corresponds to:
C. [tex]\(\frac{45}{60}\)[/tex]
Thus, the correct answer is C. [tex]\(\frac{45}{60}\)[/tex]
We have the following data:
- Total tables: 60
- Round tables: 38
- Tables by the window: 13
- Round tables by the window: 6
To find the probability of a customer being seated at a round table or by the window, we use the inclusion-exclusion principle. This principle helps us account for tables that are both round and by the window, which are counted twice if we simply add the number of round tables and window tables.
The formula to find the probability is:
[tex]\[
\text{Probability} = \frac{\text{Round tables} + \text{Window tables} - \text{Round tables by the Window}}{\text{Total tables}}
\][/tex]
Substitute the numbers into the formula:
[tex]\[
\text{Probability} = \frac{38 + 13 - 6}{60}
\][/tex]
Perform the arithmetic:
1. Add the round and window tables: [tex]\(38 + 13 = 51\)[/tex]
2. Subtract the round tables by the window: [tex]\(51 - 6 = 45\)[/tex]
So, the expression becomes:
[tex]\[
\frac{45}{60}
\][/tex]
When simplified, this fraction is equivalent to:
[tex]\[
\frac{3}{4} = 0.75
\][/tex]
Thus, the probability that a customer will be seated at a round table or by the window is 0.75. Looking at the answer choices, this probability corresponds to:
C. [tex]\(\frac{45}{60}\)[/tex]
Thus, the correct answer is C. [tex]\(\frac{45}{60}\)[/tex]
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