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Answer :
To solve this problem, we want to determine the probability that a customer will be seated at a round table or a table by the window.
Let's define:
- Total tables = 60
- Round tables = 38
- Tables by the window = 13
- Round tables by the window = 6
We use the principle of inclusion-exclusion to calculate the number of tables that are either round or by the window. This helps us avoid double-counting those tables that are both round and by the window.
1. Start by adding the number of round tables and the number of tables by the window:
[tex]\[
38 \text{ (round tables)} + 13 \text{ (window tables)} = 51
\][/tex]
2. Subtract the number of tables that are double-counted (tables that are both round and by the window):
[tex]\[
51 - 6 = 45
\][/tex]
So, there are 45 tables that are either round, by the window, or both.
Now we calculate the probability:
- The probability is the ratio of the number of tables that are round or by the window to the total number of tables.
[tex]\[
\frac{45}{60} = 0.75
\][/tex]
Therefore, the probability that a customer will be seated at a round table or by the window is [tex]\(\frac{45}{60}\)[/tex].
So, the correct answer is:
A. [tex]\(\frac{45}{60}\)[/tex]
Let's define:
- Total tables = 60
- Round tables = 38
- Tables by the window = 13
- Round tables by the window = 6
We use the principle of inclusion-exclusion to calculate the number of tables that are either round or by the window. This helps us avoid double-counting those tables that are both round and by the window.
1. Start by adding the number of round tables and the number of tables by the window:
[tex]\[
38 \text{ (round tables)} + 13 \text{ (window tables)} = 51
\][/tex]
2. Subtract the number of tables that are double-counted (tables that are both round and by the window):
[tex]\[
51 - 6 = 45
\][/tex]
So, there are 45 tables that are either round, by the window, or both.
Now we calculate the probability:
- The probability is the ratio of the number of tables that are round or by the window to the total number of tables.
[tex]\[
\frac{45}{60} = 0.75
\][/tex]
Therefore, the probability that a customer will be seated at a round table or by the window is [tex]\(\frac{45}{60}\)[/tex].
So, the correct answer is:
A. [tex]\(\frac{45}{60}\)[/tex]
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