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Answer :
Sure! Let's work through the problem step by step to find the probability that a customer will be seated at a round table or by the window.
1. Understand the Problem:
- We have a total of 60 tables in the restaurant.
- 38 of these tables are round.
- 13 tables are located by the window.
- 6 tables are round and also by the window.
2. Applying the Formula:
- To find the probability of a customer sitting at a round table or by the window, we can use the formula for the probability of the union of two events:
[tex]\[ P(\text{Round or Window}) = P(\text{Round}) + P(\text{Window}) - P(\text{Round and Window}) \][/tex]
3. Calculate Each Probability:
- Round Tables: There are 38 round tables.
- Window Tables: There are 13 tables by the window.
- Tables that are Round and by the Window: There are 6 tables that are both round and by the window.
4. Plug the Values into the Formula:
- The number of tables that are either round or by the window is:
[tex]\[ 38 + 13 - 6 = 45 \][/tex]
- Therefore, there are 45 tables that are either round or by the window.
5. Calculate the Probability:
- The probability that a randomly seated customer will be at a round table or by the window is:
[tex]\[ \frac{45}{60} \][/tex]
6. Final Answer:
- The correct answer is [tex]\(\frac{45}{60}\)[/tex], which simplifies to the fraction that represents the probability. The correct choice is A.
This means that if a table is randomly assigned, there is a [tex]\(\frac{45}{60}\)[/tex] chance that the customer will be seated at a round table or by the window.
1. Understand the Problem:
- We have a total of 60 tables in the restaurant.
- 38 of these tables are round.
- 13 tables are located by the window.
- 6 tables are round and also by the window.
2. Applying the Formula:
- To find the probability of a customer sitting at a round table or by the window, we can use the formula for the probability of the union of two events:
[tex]\[ P(\text{Round or Window}) = P(\text{Round}) + P(\text{Window}) - P(\text{Round and Window}) \][/tex]
3. Calculate Each Probability:
- Round Tables: There are 38 round tables.
- Window Tables: There are 13 tables by the window.
- Tables that are Round and by the Window: There are 6 tables that are both round and by the window.
4. Plug the Values into the Formula:
- The number of tables that are either round or by the window is:
[tex]\[ 38 + 13 - 6 = 45 \][/tex]
- Therefore, there are 45 tables that are either round or by the window.
5. Calculate the Probability:
- The probability that a randomly seated customer will be at a round table or by the window is:
[tex]\[ \frac{45}{60} \][/tex]
6. Final Answer:
- The correct answer is [tex]\(\frac{45}{60}\)[/tex], which simplifies to the fraction that represents the probability. The correct choice is A.
This means that if a table is randomly assigned, there is a [tex]\(\frac{45}{60}\)[/tex] chance that the customer will be seated at a round table or by the window.
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