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Answer :
To determine the probability that a customer will be seated at a round table or by the window, we can follow these steps:
1. Understand the Sets:
- There are a total of 60 tables.
- Out of these, 38 are round tables.
- There are 13 tables located by the window.
- Among these, 6 tables are both round and located by the window.
2. Calculate the Union of the Two Sets:
- We want the number of tables that are either round or by the window.
- To find this, we use the formula for the union of two sets:
[tex]\[
\text{Number of round or window tables} = (\text{Number of round tables}) + (\text{Number of window tables}) - (\text{Number of round tables by the window})
\][/tex]
- Plugging in the numbers we have:
[tex]\[
38 + 13 - 6 = 45
\][/tex]
3. Calculate the Probability:
- To find the probability that a customer will be seated at a round table or by the window, we divide the number of desired tables by the total number of tables:
[tex]\[
\text{Probability} = \frac{45}{60}
\][/tex]
4. Simplify the Probability:
- Simplifying the fraction [tex]\(\frac{45}{60}\)[/tex] gives us [tex]\(\frac{3}{4}\)[/tex] or, as a decimal, [tex]\(0.75\)[/tex].
Therefore, the correct answer is that the probability a customer will be seated at a round table or by the window is [tex]\(\frac{45}{60}\)[/tex], which matches option A.
1. Understand the Sets:
- There are a total of 60 tables.
- Out of these, 38 are round tables.
- There are 13 tables located by the window.
- Among these, 6 tables are both round and located by the window.
2. Calculate the Union of the Two Sets:
- We want the number of tables that are either round or by the window.
- To find this, we use the formula for the union of two sets:
[tex]\[
\text{Number of round or window tables} = (\text{Number of round tables}) + (\text{Number of window tables}) - (\text{Number of round tables by the window})
\][/tex]
- Plugging in the numbers we have:
[tex]\[
38 + 13 - 6 = 45
\][/tex]
3. Calculate the Probability:
- To find the probability that a customer will be seated at a round table or by the window, we divide the number of desired tables by the total number of tables:
[tex]\[
\text{Probability} = \frac{45}{60}
\][/tex]
4. Simplify the Probability:
- Simplifying the fraction [tex]\(\frac{45}{60}\)[/tex] gives us [tex]\(\frac{3}{4}\)[/tex] or, as a decimal, [tex]\(0.75\)[/tex].
Therefore, the correct answer is that the probability a customer will be seated at a round table or by the window is [tex]\(\frac{45}{60}\)[/tex], which matches option A.
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