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Answer :
To find the probability that a customer will be seated at a round table or by the window, we can use the addition rule for probabilities. This rule helps us calculate the probability of either of two events happening, including when they can happen at the same time.
Let's break it down:
1. Identify the Total Number of Tables:
The restaurant has a total of 60 tables.
2. Identify the Specific Groups of Tables:
- There are 38 round tables.
- There are 13 tables by the window.
- There are 6 tables that are both round and by the window.
3. Apply the Addition Rule for Probabilities:
The probability of a customer sitting at either a round table or a table by the window is calculated by adding the probabilities of these two events and then subtracting the probability of both events happening simultaneously (since those tables are counted in both categories).
The formula is:
[tex]\[
P(\text{Round or Window}) = P(\text{Round}) + P(\text{Window}) - P(\text{Round and Window})
\][/tex]
4. Substitute the Values:
- [tex]\(P(\text{Round}) = \frac{38}{60}\)[/tex]
- [tex]\(P(\text{Window}) = \frac{13}{60}\)[/tex]
- [tex]\(P(\text{Round and Window}) = \frac{6}{60}\)[/tex]
Putting it all together:
[tex]\[
P(\text{Round or Window}) = \frac{38}{60} + \frac{13}{60} - \frac{6}{60} = \frac{45}{60}
\][/tex]
5. Simplify the Probability:
[tex]\(\frac{45}{60}\)[/tex] simplifies to [tex]\(\frac{3}{4}\)[/tex], which is equal to 0.75.
Thus, the probability that a customer will be seated at a round table or by the window is 0.75. This corresponds to answer choice C, [tex]\(\frac{45}{60}\)[/tex].
Let's break it down:
1. Identify the Total Number of Tables:
The restaurant has a total of 60 tables.
2. Identify the Specific Groups of Tables:
- There are 38 round tables.
- There are 13 tables by the window.
- There are 6 tables that are both round and by the window.
3. Apply the Addition Rule for Probabilities:
The probability of a customer sitting at either a round table or a table by the window is calculated by adding the probabilities of these two events and then subtracting the probability of both events happening simultaneously (since those tables are counted in both categories).
The formula is:
[tex]\[
P(\text{Round or Window}) = P(\text{Round}) + P(\text{Window}) - P(\text{Round and Window})
\][/tex]
4. Substitute the Values:
- [tex]\(P(\text{Round}) = \frac{38}{60}\)[/tex]
- [tex]\(P(\text{Window}) = \frac{13}{60}\)[/tex]
- [tex]\(P(\text{Round and Window}) = \frac{6}{60}\)[/tex]
Putting it all together:
[tex]\[
P(\text{Round or Window}) = \frac{38}{60} + \frac{13}{60} - \frac{6}{60} = \frac{45}{60}
\][/tex]
5. Simplify the Probability:
[tex]\(\frac{45}{60}\)[/tex] simplifies to [tex]\(\frac{3}{4}\)[/tex], which is equal to 0.75.
Thus, the probability that a customer will be seated at a round table or by the window is 0.75. This corresponds to answer choice C, [tex]\(\frac{45}{60}\)[/tex].
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