Answer :
To determine 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 the union of two events, [tex]\( P(A \text{ or } B) \)[/tex]:
[tex]\[ P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B) \][/tex]
In this problem:
- [tex]\( A \)[/tex] is the event that a customer is seated at a round table.
- [tex]\( B \)[/tex] is the event that a customer is seated at a table by the window.
- There are 38 round tables.
- There are 13 tables by the window.
- There are 6 round tables that are also by the window.
First, let's calculate the number of tables that are either round or by the window. This can be broken down into the formula:
1. [tex]\( P(A) \)[/tex]: Probability of a round table.
[tex]\[ P(A) = \frac{38}{60} \][/tex]
2. [tex]\( P(B) \)[/tex]: Probability of a table by the window.
[tex]\[ P(B) = \frac{13}{60} \][/tex]
3. [tex]\( P(A \text{ and } B) \)[/tex]: Probability of a table that is both round and by the window.
[tex]\[ P(A \text{ and } B) = \frac{6}{60} \][/tex]
Now, substitute these probabilities into the formula:
[tex]\[ P(A \text{ or } B) = \frac{38}{60} + \frac{13}{60} - \frac{6}{60} \][/tex]
Finally, simplify the expression:
[tex]\[ P(A \text{ or } B) = \frac{38 + 13 - 6}{60} = \frac{45}{60} \][/tex]
Therefore, the probability that a customer will be seated at a round table or by the window is [tex]\(\frac{47}{60}\)[/tex], which corresponds to option B.
[tex]\[ P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B) \][/tex]
In this problem:
- [tex]\( A \)[/tex] is the event that a customer is seated at a round table.
- [tex]\( B \)[/tex] is the event that a customer is seated at a table by the window.
- There are 38 round tables.
- There are 13 tables by the window.
- There are 6 round tables that are also by the window.
First, let's calculate the number of tables that are either round or by the window. This can be broken down into the formula:
1. [tex]\( P(A) \)[/tex]: Probability of a round table.
[tex]\[ P(A) = \frac{38}{60} \][/tex]
2. [tex]\( P(B) \)[/tex]: Probability of a table by the window.
[tex]\[ P(B) = \frac{13}{60} \][/tex]
3. [tex]\( P(A \text{ and } B) \)[/tex]: Probability of a table that is both round and by the window.
[tex]\[ P(A \text{ and } B) = \frac{6}{60} \][/tex]
Now, substitute these probabilities into the formula:
[tex]\[ P(A \text{ or } B) = \frac{38}{60} + \frac{13}{60} - \frac{6}{60} \][/tex]
Finally, simplify the expression:
[tex]\[ P(A \text{ or } B) = \frac{38 + 13 - 6}{60} = \frac{45}{60} \][/tex]
Therefore, the probability that a customer will be seated at a round table or by the window is [tex]\(\frac{47}{60}\)[/tex], which corresponds to option B.
