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Answer :
Let's solve this step-by-step.
Here are the given details:
- Total number of tables in the restaurant: 60
- Number of round tables: 38
- Number of tables by the window: 13
- Number of round tables by the window: 6
We need to find the probability of a table being either round or by the window. We can denote this as [tex]\( P(\text{round or window}) \)[/tex].
Using the principle of inclusion and exclusion for probabilities, we know:
[tex]\[ P(\text{round or window}) = P(\text{round}) + P(\text{window}) - P(\text{round and window}) \][/tex]
Let's break down each of these probabilities:
1. Probability of a round table:
[tex]\[
P(\text{round}) = \frac{\text{Number of round tables}}{\text{Total number of tables}} = \frac{38}{60}
\][/tex]
2. Probability of a table by the window:
[tex]\[
P(\text{window}) = \frac{\text{Number of tables by the window}}{\text{Total number of tables}} = \frac{13}{60}
\][/tex]
3. Probability of a round table by the window:
[tex]\[
P(\text{round and window}) = \frac{\text{Number of round tables by the window}}{\text{Total number of tables}} = \frac{6}{60}
\][/tex]
Now, let's use the formula:
[tex]\[
P(\text{round or window}) = \frac{38}{60} + \frac{13}{60} - \frac{6}{60}
\][/tex]
To simplify, 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].
Therefore, the correct answer is:
[tex]\[
\boxed{\frac{45}{60}}
\][/tex]
So, the correct answer is A.
Here are the given details:
- Total number of tables in the restaurant: 60
- Number of round tables: 38
- Number of tables by the window: 13
- Number of round tables by the window: 6
We need to find the probability of a table being either round or by the window. We can denote this as [tex]\( P(\text{round or window}) \)[/tex].
Using the principle of inclusion and exclusion for probabilities, we know:
[tex]\[ P(\text{round or window}) = P(\text{round}) + P(\text{window}) - P(\text{round and window}) \][/tex]
Let's break down each of these probabilities:
1. Probability of a round table:
[tex]\[
P(\text{round}) = \frac{\text{Number of round tables}}{\text{Total number of tables}} = \frac{38}{60}
\][/tex]
2. Probability of a table by the window:
[tex]\[
P(\text{window}) = \frac{\text{Number of tables by the window}}{\text{Total number of tables}} = \frac{13}{60}
\][/tex]
3. Probability of a round table by the window:
[tex]\[
P(\text{round and window}) = \frac{\text{Number of round tables by the window}}{\text{Total number of tables}} = \frac{6}{60}
\][/tex]
Now, let's use the formula:
[tex]\[
P(\text{round or window}) = \frac{38}{60} + \frac{13}{60} - \frac{6}{60}
\][/tex]
To simplify, 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].
Therefore, the correct answer is:
[tex]\[
\boxed{\frac{45}{60}}
\][/tex]
So, the correct answer is A.
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