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Answer :
To solve the problem of finding the probability that a customer will be seated at a round table or by the window, we can use the formula for the probability of either event A or event B occurring. This is given by:
[tex]\[ P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B) \][/tex]
In this scenario:
- Event A is the table being round.
- Event B is the table being by the window.
From the problem, we know:
- There are 38 round tables.
- There are 13 tables by the window.
- There are 6 tables that are both round and by the window.
- The total number of tables is 60.
Let's apply these numbers to the formula:
1. [tex]\( P(A) \)[/tex], the probability of a table being round, is [tex]\(\frac{38}{60}\)[/tex].
2. [tex]\( P(B) \)[/tex], the probability of a table being by the window, is [tex]\(\frac{13}{60}\)[/tex].
3. [tex]\( P(A \text{ and } B) \)[/tex], the probability of a table being both round and by the window, is [tex]\(\frac{6}{60}\)[/tex].
Substitute these into the formula:
[tex]\[ P(\text{round or by the window}) = \frac{38}{60} + \frac{13}{60} - \frac{6}{60} \][/tex]
Combine the fractions:
[tex]\[ P(\text{round or by the window}) = \frac{38 + 13 - 6}{60} = \frac{45}{60} \][/tex]
Simplify the fraction:
[tex]\[ P(\text{round or by the window}) = \frac{3}{4} = 0.75 \][/tex]
Thus, the probability that a customer will be seated at a round table or by the window is [tex]\(\frac{45}{60}\)[/tex], which matches option D. Therefore, the correct answer is:
D. [tex]\(\frac{45}{60}\)[/tex]
[tex]\[ P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B) \][/tex]
In this scenario:
- Event A is the table being round.
- Event B is the table being by the window.
From the problem, we know:
- There are 38 round tables.
- There are 13 tables by the window.
- There are 6 tables that are both round and by the window.
- The total number of tables is 60.
Let's apply these numbers to the formula:
1. [tex]\( P(A) \)[/tex], the probability of a table being round, is [tex]\(\frac{38}{60}\)[/tex].
2. [tex]\( P(B) \)[/tex], the probability of a table being by the window, is [tex]\(\frac{13}{60}\)[/tex].
3. [tex]\( P(A \text{ and } B) \)[/tex], the probability of a table being both round and by the window, is [tex]\(\frac{6}{60}\)[/tex].
Substitute these into the formula:
[tex]\[ P(\text{round or by the window}) = \frac{38}{60} + \frac{13}{60} - \frac{6}{60} \][/tex]
Combine the fractions:
[tex]\[ P(\text{round or by the window}) = \frac{38 + 13 - 6}{60} = \frac{45}{60} \][/tex]
Simplify the fraction:
[tex]\[ P(\text{round or by the window}) = \frac{3}{4} = 0.75 \][/tex]
Thus, the probability that a customer will be seated at a round table or by the window is [tex]\(\frac{45}{60}\)[/tex], which matches option D. Therefore, the correct answer is:
D. [tex]\(\frac{45}{60}\)[/tex]
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