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Answer :
To solve this problem, we want to find the probability that a customer will be seated at either a round table or by the window.
Let's break down the steps:
1. Identify the Events:
- Let event A be the event of being seated at a round table. There are 38 round tables.
- Let event B be the event of being seated by the window. There are 13 tables by the window.
- There are 6 tables that are both round and by the window.
2. Total Number of Tables:
- There are a total of 60 tables in the restaurant.
3. Formula for Probability of A or B:
- To find the probability of either event A or event B happening, we use the formula:
[tex]\[
P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)
\][/tex]
- Here, [tex]\( P(A) \)[/tex] is the probability of a round table and [tex]\( P(B) \)[/tex] is the probability of a table by the window.
4. Calculate Probabilities of Each Event:
- Number of round tables, [tex]\( P(A) = \frac{38}{60} \)[/tex].
- Number of tables by the window, [tex]\( P(B) = \frac{13}{60} \)[/tex].
- Number of tables that are both round and by the window, [tex]\( P(A \text{ and } B) = \frac{6}{60} \)[/tex].
5. Substitute and Solve:
- Substitute these into the probability formula:
[tex]\[
P(A \text{ or } B) = \frac{38}{60} + \frac{13}{60} - \frac{6}{60}
\][/tex]
6. Compute the Probability:
- Simplify the expression:
[tex]\[
P(A \text{ or } B) = \frac{38 + 13 - 6}{60} = \frac{45}{60}
\][/tex]
- Simplifying [tex]\(\frac{45}{60}\)[/tex] gives [tex]\(\frac{3}{4}\)[/tex] or 0.75.
Therefore, the probability that a customer will be seated at a round table or by the window is [tex]\(\frac{3}{4}\)[/tex], which corresponds to option A: [tex]\(\frac{45}{60}\)[/tex].
Let's break down the steps:
1. Identify the Events:
- Let event A be the event of being seated at a round table. There are 38 round tables.
- Let event B be the event of being seated by the window. There are 13 tables by the window.
- There are 6 tables that are both round and by the window.
2. Total Number of Tables:
- There are a total of 60 tables in the restaurant.
3. Formula for Probability of A or B:
- To find the probability of either event A or event B happening, we use the formula:
[tex]\[
P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)
\][/tex]
- Here, [tex]\( P(A) \)[/tex] is the probability of a round table and [tex]\( P(B) \)[/tex] is the probability of a table by the window.
4. Calculate Probabilities of Each Event:
- Number of round tables, [tex]\( P(A) = \frac{38}{60} \)[/tex].
- Number of tables by the window, [tex]\( P(B) = \frac{13}{60} \)[/tex].
- Number of tables that are both round and by the window, [tex]\( P(A \text{ and } B) = \frac{6}{60} \)[/tex].
5. Substitute and Solve:
- Substitute these into the probability formula:
[tex]\[
P(A \text{ or } B) = \frac{38}{60} + \frac{13}{60} - \frac{6}{60}
\][/tex]
6. Compute the Probability:
- Simplify the expression:
[tex]\[
P(A \text{ or } B) = \frac{38 + 13 - 6}{60} = \frac{45}{60}
\][/tex]
- Simplifying [tex]\(\frac{45}{60}\)[/tex] gives [tex]\(\frac{3}{4}\)[/tex] or 0.75.
Therefore, the probability that a customer will be seated at a round table or by the window is [tex]\(\frac{3}{4}\)[/tex], which corresponds to option A: [tex]\(\frac{45}{60}\)[/tex].
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