Answer :
Sure, I'd be happy to explain the solution step-by-step!
1. Understanding the Problem:
- We need to find the probability that a customer will be seated at either a round table or a table by the window.
- We have the following numbers:
- Total tables: 60
- Round tables: 38
- Tables by the window: 13
- Round tables by the window: 6
2. Calculate the Total Number of Tables that are Either Round or by the Window:
- First, find the number of tables that are either round or located by the window.
- When you add the number of round tables and the number of tables by the window, you are counting the round tables by the window twice.
- So, you need to subtract the double-counted tables (round tables by the window).
Number of tables that are round or by the window:
[tex]\[
38 \text{ (round tables)} + 13 \text{ (window tables)} - 6 \text{ (round tables by the window)} = 45
\][/tex]
3. Calculate the Probability:
- The probability is the ratio of the number of favorable outcomes (tables that are round or by the window) to the total number of outcomes (total tables).
- So, the probability [tex]\( P \)[/tex] that a customer will be seated at a round table or by the window is:
[tex]\[
P = \frac{\text{Number of tables that are round or by the window}}{\text{Total number of tables}} = \frac{45}{60}
\][/tex]
4. Simplify the Fraction:
- Simplify [tex]\(\frac{45}{60}\)[/tex] to its lowest terms:
[tex]\[
\frac{45}{60} = \frac{3}{4}
\][/tex]
Converting [tex]\( \frac{3}{4} \)[/tex] to a decimal, we get 0.75.
5. Select the Correct Answer:
- From the given choices:
- [tex]\(\frac{29}{60}\)[/tex]
- [tex]\(\frac{41}{60}\)[/tex]
- [tex]\(\frac{45}{60}\)[/tex]
- [tex]\(\frac{47}{60}\)[/tex]
The correct answer is [tex]\(\frac{45}{60}\)[/tex], which corresponds to:
[tex]\[
\frac{3}{4} = 0.75
\][/tex]
So, the correct answer is C. [tex]\(\frac{45}{60}\)[/tex].
1. Understanding the Problem:
- We need to find the probability that a customer will be seated at either a round table or a table by the window.
- We have the following numbers:
- Total tables: 60
- Round tables: 38
- Tables by the window: 13
- Round tables by the window: 6
2. Calculate the Total Number of Tables that are Either Round or by the Window:
- First, find the number of tables that are either round or located by the window.
- When you add the number of round tables and the number of tables by the window, you are counting the round tables by the window twice.
- So, you need to subtract the double-counted tables (round tables by the window).
Number of tables that are round or by the window:
[tex]\[
38 \text{ (round tables)} + 13 \text{ (window tables)} - 6 \text{ (round tables by the window)} = 45
\][/tex]
3. Calculate the Probability:
- The probability is the ratio of the number of favorable outcomes (tables that are round or by the window) to the total number of outcomes (total tables).
- So, the probability [tex]\( P \)[/tex] that a customer will be seated at a round table or by the window is:
[tex]\[
P = \frac{\text{Number of tables that are round or by the window}}{\text{Total number of tables}} = \frac{45}{60}
\][/tex]
4. Simplify the Fraction:
- Simplify [tex]\(\frac{45}{60}\)[/tex] to its lowest terms:
[tex]\[
\frac{45}{60} = \frac{3}{4}
\][/tex]
Converting [tex]\( \frac{3}{4} \)[/tex] to a decimal, we get 0.75.
5. Select the Correct Answer:
- From the given choices:
- [tex]\(\frac{29}{60}\)[/tex]
- [tex]\(\frac{41}{60}\)[/tex]
- [tex]\(\frac{45}{60}\)[/tex]
- [tex]\(\frac{47}{60}\)[/tex]
The correct answer is [tex]\(\frac{45}{60}\)[/tex], which corresponds to:
[tex]\[
\frac{3}{4} = 0.75
\][/tex]
So, the correct answer is C. [tex]\(\frac{45}{60}\)[/tex].
