College

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. There are 6 round tables by the window.

If tables are randomly assigned to customers, what is the probability that a customer will be seated at a round table or by the window?

A. [tex]\frac{29}{60}[/tex]
B. [tex]\frac{47}{60}[/tex]
C. [tex]\frac{45}{60}[/tex]
D. [tex]\frac{41}{60}[/tex]

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.