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Answer :
To solve the problem of finding the probability that a customer will be seated at a round table or by the window, we can follow these steps:
1. Understand the Events:
- Round tables: 38
- Tables by the window: 13
- Round tables by the window: 6
2. Use the Principle of Inclusion-Exclusion:
- To find the total number of tables that are either round or by the window, we need to add the number of round tables to the number of window tables, and then subtract the tables that are both round and by the window since they have been counted twice.
- Formula: [tex]\( \text{Round or Window Tables} = (\text{Round Tables}) + (\text{Window Tables}) - (\text{Round and Window Tables}) \)[/tex]
3. Plug in the Values:
- [tex]\( \text{Round or Window Tables} = 38 + 13 - 6 = 45 \)[/tex]
4. Calculate the Probability:
- The probability that a customer will be seated at a table that is either round or by the window is the number of tables fitting this criterion divided by the total number of tables.
- Total tables = 60
- Probability = [tex]\( \frac{45}{60} = \frac{3}{4} = 0.75 \)[/tex]
So, 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 0.75. Therefore, the correct answer is:
B. [tex]\(\frac{45}{60}\)[/tex]
1. Understand the Events:
- Round tables: 38
- Tables by the window: 13
- Round tables by the window: 6
2. Use the Principle of Inclusion-Exclusion:
- To find the total number of tables that are either round or by the window, we need to add the number of round tables to the number of window tables, and then subtract the tables that are both round and by the window since they have been counted twice.
- Formula: [tex]\( \text{Round or Window Tables} = (\text{Round Tables}) + (\text{Window Tables}) - (\text{Round and Window Tables}) \)[/tex]
3. Plug in the Values:
- [tex]\( \text{Round or Window Tables} = 38 + 13 - 6 = 45 \)[/tex]
4. Calculate the Probability:
- The probability that a customer will be seated at a table that is either round or by the window is the number of tables fitting this criterion divided by the total number of tables.
- Total tables = 60
- Probability = [tex]\( \frac{45}{60} = \frac{3}{4} = 0.75 \)[/tex]
So, 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 0.75. Therefore, the correct answer is:
B. [tex]\(\frac{45}{60}\)[/tex]
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