Answer :
To solve this problem, we need to determine the probability that a customer will be seated at either a round table or a table by the window. We can use the inclusion-exclusion principle to make this calculation.
Here's a step-by-step solution:
1. Define Total Tables:
- The restaurant has a total of 60 tables.
2. Identify Round Tables:
- There are 38 round tables.
3. Identify Window Tables:
- There are 13 tables by the window.
4. Identify Round Tables by the Window:
- There are 6 tables that are both round and by the window.
5. Use the Inclusion-Exclusion Principle:
- To find the total number of tables that are either round or by the window, we use:
[tex]\[
(\text{Number of Round Tables}) + (\text{Number of Window Tables}) - (\text{Number of Round Tables by the Window})
\][/tex]
- Substitute the numbers into this formula:
[tex]\[
38 + 13 - 6 = 45
\][/tex]
6. Calculate the Probability:
- Probability is defined as the number of favorable outcomes divided by the total number of possible outcomes.
- Therefore, the probability that a customer will be seated at a round table or by the window is:
[tex]\[
\frac{45}{60}
\][/tex]
7. Simplify the Fraction:
- Simplifying [tex]\(\frac{45}{60}\)[/tex], we divide both the numerator and denominator by their greatest common divisor, which is 15:
[tex]\[
\frac{45}{60} = \frac{3}{4} = 0.75
\][/tex]
Thus, the probability that a customer will be seated at a round table or a table by the window is 0.75, which matches option B.
Here's a step-by-step solution:
1. Define Total Tables:
- The restaurant has a total of 60 tables.
2. Identify Round Tables:
- There are 38 round tables.
3. Identify Window Tables:
- There are 13 tables by the window.
4. Identify Round Tables by the Window:
- There are 6 tables that are both round and by the window.
5. Use the Inclusion-Exclusion Principle:
- To find the total number of tables that are either round or by the window, we use:
[tex]\[
(\text{Number of Round Tables}) + (\text{Number of Window Tables}) - (\text{Number of Round Tables by the Window})
\][/tex]
- Substitute the numbers into this formula:
[tex]\[
38 + 13 - 6 = 45
\][/tex]
6. Calculate the Probability:
- Probability is defined as the number of favorable outcomes divided by the total number of possible outcomes.
- Therefore, the probability that a customer will be seated at a round table or by the window is:
[tex]\[
\frac{45}{60}
\][/tex]
7. Simplify the Fraction:
- Simplifying [tex]\(\frac{45}{60}\)[/tex], we divide both the numerator and denominator by their greatest common divisor, which is 15:
[tex]\[
\frac{45}{60} = \frac{3}{4} = 0.75
\][/tex]
Thus, the probability that a customer will be seated at a round table or a table by the window is 0.75, which matches option B.
