Answer :
Sure, let's solve this problem step-by-step.
First, we need to determine the probability that a customer will be seated at either a round table or a table by the window.
We are given the following information:
- Total tables: 60
- Round tables: 38
- Tables by the window: 13
- Round tables by the window: 6
We want to find the probability of a table being either round or by the window. For this, we can use the formula for the union of two events:
[tex]\[ P(\text{Round or Window}) = P(\text{Round}) + P(\text{Window}) - P(\text{Round and Window}) \][/tex]
Let's break it down:
1. Calculate the number of round tables and window tables, without double-counting the tables that are both:
- Tables that are round: 38
- Tables that are by the window: 13
- Tables that are both round and by the window: 6
So, we use the formula:
[tex]\[ \text{Total (Round or Window)} = \text{Round tables} + \text{Tables by the window} - \text{Tables that are both} \][/tex]
Substituting the values:
[tex]\[ \text{Total (Round or Window)} = 38 + 13 - 6 = 45 \][/tex]
2. Calculate the probability:
[tex]\[ P(\text{Round or Window}) = \frac{\text{Total (Round or Window)}}{\text{Total tables}} = \frac{45}{60} \][/tex]
Thus, the probability that a customer will be seated at a round table or by the window is:
[tex]\[ \frac{45}{60} \][/tex]
So, the correct answer is:
A. [tex]\(\frac{45}{60}\)[/tex]
First, we need to determine the probability that a customer will be seated at either a round table or a table by the window.
We are given the following information:
- Total tables: 60
- Round tables: 38
- Tables by the window: 13
- Round tables by the window: 6
We want to find the probability of a table being either round or by the window. For this, we can use the formula for the union of two events:
[tex]\[ P(\text{Round or Window}) = P(\text{Round}) + P(\text{Window}) - P(\text{Round and Window}) \][/tex]
Let's break it down:
1. Calculate the number of round tables and window tables, without double-counting the tables that are both:
- Tables that are round: 38
- Tables that are by the window: 13
- Tables that are both round and by the window: 6
So, we use the formula:
[tex]\[ \text{Total (Round or Window)} = \text{Round tables} + \text{Tables by the window} - \text{Tables that are both} \][/tex]
Substituting the values:
[tex]\[ \text{Total (Round or Window)} = 38 + 13 - 6 = 45 \][/tex]
2. Calculate the probability:
[tex]\[ P(\text{Round or Window}) = \frac{\text{Total (Round or Window)}}{\text{Total tables}} = \frac{45}{60} \][/tex]
Thus, the probability that a customer will be seated at a round table or by the window is:
[tex]\[ \frac{45}{60} \][/tex]
So, the correct answer is:
A. [tex]\(\frac{45}{60}\)[/tex]