We appreciate your visit to Select the correct answer A restaurant has a total of 60 tables Of those tables 38 are round and 13 are located by the window. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
To find the probability that a customer will be seated at either a round table or by the window, we can use the inclusion-exclusion principle. Here's a step-by-step explanation:
1. Identify the Total Number of Tables: The restaurant has a total of 60 tables.
2. Identify Tables That Are Round or by the Window:
- There are 38 round tables.
- There are 13 tables by the window.
3. Consider Overlap (Round Tables by the Window):
- There are 6 round tables located by the window. This means some tables are counted in both the round and window categories.
4. Apply the Inclusion-Exclusion Principle:
- To avoid double-counting, we use the inclusion-exclusion principle:
[tex]\[
\text{Total (Round or Window) Tables} = \text{Round Tables} + \text{Window Tables} - \text{Round and Window Tables}
\][/tex]
- Substitute the given values:
[tex]\[
= 38 + 13 - 6
\][/tex]
[tex]\[
= 45
\][/tex]
5. Calculate Probability:
- The probability that a customer will be seated at a table that is either round or by the window is the number of favorable outcomes (tables that are either round or by the window) divided by the total number of tables.
[tex]\[
\text{Probability} = \frac{45}{60}
\][/tex]
6. Simplify the Fraction:
- Simplifying [tex]\(\frac{45}{60}\)[/tex] by dividing both the numerator and denominator by their greatest common divisor, 15, we get:
[tex]\[
\frac{45 \div 15}{60 \div 15} = \frac{3}{4} = 0.75
\][/tex]
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] or 0.75. Therefore, the correct answer is:
B. [tex]\(\frac{47}{60}\)[/tex]
1. Identify the Total Number of Tables: The restaurant has a total of 60 tables.
2. Identify Tables That Are Round or by the Window:
- There are 38 round tables.
- There are 13 tables by the window.
3. Consider Overlap (Round Tables by the Window):
- There are 6 round tables located by the window. This means some tables are counted in both the round and window categories.
4. Apply the Inclusion-Exclusion Principle:
- To avoid double-counting, we use the inclusion-exclusion principle:
[tex]\[
\text{Total (Round or Window) Tables} = \text{Round Tables} + \text{Window Tables} - \text{Round and Window Tables}
\][/tex]
- Substitute the given values:
[tex]\[
= 38 + 13 - 6
\][/tex]
[tex]\[
= 45
\][/tex]
5. Calculate Probability:
- The probability that a customer will be seated at a table that is either round or by the window is the number of favorable outcomes (tables that are either round or by the window) divided by the total number of tables.
[tex]\[
\text{Probability} = \frac{45}{60}
\][/tex]
6. Simplify the Fraction:
- Simplifying [tex]\(\frac{45}{60}\)[/tex] by dividing both the numerator and denominator by their greatest common divisor, 15, we get:
[tex]\[
\frac{45 \div 15}{60 \div 15} = \frac{3}{4} = 0.75
\][/tex]
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] or 0.75. Therefore, the correct answer is:
B. [tex]\(\frac{47}{60}\)[/tex]
Thanks for taking the time to read Select the correct answer A restaurant has a total of 60 tables Of those tables 38 are round and 13 are located by the window. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
