High School

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

Answer :

To find the probability that a customer will be seated at a round table or by the window, we need to use the principle of inclusion-exclusion. Here's a step-by-step explanation:

1. Identify the total number of tables:
- The restaurant has a total of 60 tables.

2. Determine the number of round tables and window tables:
- There are 38 round tables.
- There are 13 tables that are located by the window.

3. Find the overlap (both round and by the window):
- There are 6 tables that are both round and located by the window.

4. Apply the principle of inclusion-exclusion:
- To find the number of tables that are either round or located by the window, we need to add the number of round tables and window tables, then subtract the overlap (tables that are counted twice because they meet both criteria).

5. Perform the calculation:
- Round tables = 38
- Window tables = 13
- Overlap (round and window) = 6
- Total round or window tables = Round tables + Window tables - Overlap
- Total round or window tables = 38 + 13 - 6 = 45

6. Calculate the probability:
- Probability = (Number of round or window tables) / (Total number of tables)
- Probability = 45 / 60

7. Simplify the fraction:
- 45 out of 60 simplifies to 3/4.

So, the probability that a customer will be seated at a round table or by the window is [tex]\(\frac{45}{60}\)[/tex], or option A.

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