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Answer :
To solve this problem, we want to find the probability that a customer will be seated at a round table or by the window. We can use the formula for finding the probability of events "A or B":
[tex]\[ P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B) \][/tex]
Where:
- [tex]\( P(A) \)[/tex] is the probability of being seated at a round table.
- [tex]\( P(B) \)[/tex] is the probability of being seated by the window.
- [tex]\( P(A \text{ and } B) \)[/tex] is the probability of being seated at a table that is both round and by the window.
Step 1: Define the Events
- Total tables = 60
- Round tables = 38 ([tex]\(P(A)\)[/tex])
- Window tables = 13 ([tex]\(P(B)\)[/tex])
- Round and by the window = 6 ([tex]\(P(A \text{ and } B)\)[/tex])
Step 2: Calculate the Individual Probabilities
- Probability of choosing a round table:
[tex]\[ P(A) = \frac{38}{60} \][/tex]
- Probability of choosing a table by the window:
[tex]\[ P(B) = \frac{13}{60} \][/tex]
- Probability of choosing a table that is both round and by the window:
[tex]\[ P(A \text{ and } B) = \frac{6}{60} \][/tex]
Step 3: Use the Formula for [tex]\( P(A \text{ or } B) \)[/tex]
[tex]\[ P(A \text{ or } B) = \frac{38}{60} + \frac{13}{60} - \frac{6}{60} \][/tex]
Step 4: Simplify the Expression
Add the probabilities:
[tex]\[
P(A \text{ or } B) = \frac{38 + 13 - 6}{60} = \frac{45}{60}
\][/tex]
Step 5: Final Answer
The probability that a customer will be seated at a round table or by the window is [tex]\(\frac{45}{60}\)[/tex], which simplifies to [tex]\(\frac{3}{4}\)[/tex].
Thus, the correct answer is:
B. [tex]\(\frac{45}{60}\)[/tex]
[tex]\[ P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B) \][/tex]
Where:
- [tex]\( P(A) \)[/tex] is the probability of being seated at a round table.
- [tex]\( P(B) \)[/tex] is the probability of being seated by the window.
- [tex]\( P(A \text{ and } B) \)[/tex] is the probability of being seated at a table that is both round and by the window.
Step 1: Define the Events
- Total tables = 60
- Round tables = 38 ([tex]\(P(A)\)[/tex])
- Window tables = 13 ([tex]\(P(B)\)[/tex])
- Round and by the window = 6 ([tex]\(P(A \text{ and } B)\)[/tex])
Step 2: Calculate the Individual Probabilities
- Probability of choosing a round table:
[tex]\[ P(A) = \frac{38}{60} \][/tex]
- Probability of choosing a table by the window:
[tex]\[ P(B) = \frac{13}{60} \][/tex]
- Probability of choosing a table that is both round and by the window:
[tex]\[ P(A \text{ and } B) = \frac{6}{60} \][/tex]
Step 3: Use the Formula for [tex]\( P(A \text{ or } B) \)[/tex]
[tex]\[ P(A \text{ or } B) = \frac{38}{60} + \frac{13}{60} - \frac{6}{60} \][/tex]
Step 4: Simplify the Expression
Add the probabilities:
[tex]\[
P(A \text{ or } B) = \frac{38 + 13 - 6}{60} = \frac{45}{60}
\][/tex]
Step 5: Final Answer
The probability that a customer will be seated at a round table or by the window is [tex]\(\frac{45}{60}\)[/tex], which simplifies to [tex]\(\frac{3}{4}\)[/tex].
Thus, the correct answer is:
B. [tex]\(\frac{45}{60}\)[/tex]
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