Answer :
To find the probability that a customer will be seated at a round table or by the window, we can use the principle of inclusion and exclusion. This principle helps us account for overlapping categories—in this case, the round tables that are also by the window.
Here's how we calculate it step-by-step:
1. Identify Total Number of Tables:
The restaurant has a total of 60 tables.
2. Calculate Probability for Round Tables:
There are 38 round tables.
Probability of a table being round = Number of round tables / Total number of tables = 38/60.
3. Calculate Probability for Tables by the Window:
There are 13 tables by the window.
Probability of a table being by the window = Number of window tables / Total number of tables = 13/60.
4. Consider Overlap (Round Tables by the Window):
There are 6 tables that are both round and by the window.
Probability of a table being both round and by the window = Number of round and window tables / Total number of tables = 6/60.
5. Apply the Inclusion-Exclusion Principle:
To find the probability of a table being round or by the window, we add the probabilities of the two events and subtract the overlap (since it was counted twice):
Probability of a table being round or by the window = Probability of round + Probability of window - Probability of both.
Substituting the values:
[tex]\[
P(\text{round or window}) = \frac{38}{60} + \frac{13}{60} - \frac{6}{60}
\][/tex]
[tex]\[
P(\text{round or window}) = \frac{38 + 13 - 6}{60} = \frac{45}{60}
\][/tex]
6. Conclusion:
Therefore, the probability that a customer will be seated at a round table or by the window is [tex]\(\frac{45}{60}\)[/tex].
So, the correct answer is B. [tex]\(\frac{45}{60}\)[/tex].
Here's how we calculate it step-by-step:
1. Identify Total Number of Tables:
The restaurant has a total of 60 tables.
2. Calculate Probability for Round Tables:
There are 38 round tables.
Probability of a table being round = Number of round tables / Total number of tables = 38/60.
3. Calculate Probability for Tables by the Window:
There are 13 tables by the window.
Probability of a table being by the window = Number of window tables / Total number of tables = 13/60.
4. Consider Overlap (Round Tables by the Window):
There are 6 tables that are both round and by the window.
Probability of a table being both round and by the window = Number of round and window tables / Total number of tables = 6/60.
5. Apply the Inclusion-Exclusion Principle:
To find the probability of a table being round or by the window, we add the probabilities of the two events and subtract the overlap (since it was counted twice):
Probability of a table being round or by the window = Probability of round + Probability of window - Probability of both.
Substituting the values:
[tex]\[
P(\text{round or window}) = \frac{38}{60} + \frac{13}{60} - \frac{6}{60}
\][/tex]
[tex]\[
P(\text{round or window}) = \frac{38 + 13 - 6}{60} = \frac{45}{60}
\][/tex]
6. Conclusion:
Therefore, the probability that a customer will be seated at a round table or by the window is [tex]\(\frac{45}{60}\)[/tex].
So, the correct answer is B. [tex]\(\frac{45}{60}\)[/tex].
