CHECK ANSWERS PLEASE
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Paula asked 30 students what they ate for lunch.
All the students had at least a sandwich, salad or fruit.
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QUESTION A
Draw a Venn Diagram.
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THIS IS THE INFORMATION FROM THE DIAGRAM:
5 students had a sandwich, salad and fruit.
3 students had a sandwich only.
7 students had salad only.
7 students had fruit only.
4 students had a sandwich and salad.
2 students had a sandwich and fruit.
2 students had salad and fruit.
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1 person is now chosen at random.
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QUESTION B
Find the probability that they have a sandwich but not fruit.
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ANSWER: 7/30?
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QUESTION C
Given that the person has salad, find the probability that they also have fruit.
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ANSWER: 7/18 or 7/25 or 7/30 or 7/14 = 1/2?
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Tyfy
Let's check the answers step by step.
QUESTION A: The Venn diagram represents the information provided. From the diagram, we can see that there are 5 students in the intersection of sandwich, salad, and fruit. There are 3 students in the sandwich-only category, 7 students in the salad-only category, and 7 students in the fruit-only category. Additionally, there are 4 students in the intersection of sandwich and salad, 2 students in the intersection of sandwich and fruit, and 2 students in the intersection of salad and fruit.
QUESTION B: The probability that a randomly chosen person has a sandwich but not fruit can be calculated as the number of people with a sandwich only divided by the total number of students. From the diagram, we see that there are 3 students who have a sandwich only, so the probability is 3/30, which simplifies to 1/10.
ANSWER: The correct probability is 1/10, not 7/30.
QUESTION C: The probability that a person has fruit given that they have salad can be calculated as the number of people with both salad and fruit divided by the number of people with salad. From the diagram, we see that there are 2 students with salad and fruit, and a total of 7 students with salad. So, the probability is 2/7.
ANSWER: The correct probability is 2/7.
Let's summarize the answers:
QUESTION B: The probability that they have a sandwich but not fruit is 1/10.
QUESTION C: The probability that they have fruit given that they have salad is 2/7.
Let's check the answers for each question:
Question A: Draw a Venn Diagram
The information given in the diagram is as follows:
- 5 students had a sandwich, salad, and fruit (intersection of all three categories).
- 3 students had a sandwich only.
- 7 students had salad only.
- 7 students had fruit only.
- 4 students had a sandwich and salad.
- 2 students had a sandwich and fruit.
- 2 students had salad and fruit.
To draw the Venn Diagram, you would create three circles to represent the categories: sandwich, salad, and fruit. The intersection of all three circles would represent the 5 students who had a sandwich, salad, and fruit. The other regions inside the circles would represent the number of students who had the specific combination or only one category. Make sure the numbers mentioned for each category are placed correctly in the diagram.
Question B: Find the probability that they have a sandwich but not fruit.
To calculate the probability, we need to know the total number of students surveyed (which is 30 in this case) and the number of students who have a sandwich but not fruit. According to the given information, 3 students had a sandwich only. Therefore, the probability would be 3/30, which simplifies to 1/10.
Answer: 1/10
Question C: Given that the person has salad, find the probability that they also have fruit.
To calculate the probability, we need to know the number of students who have salad and fruit and the total number of students who have salad. According to the given information, 2 students had salad and fruit, and there were 7 students who had salad only.
Therefore, the probability would be 2/7.
Answer: 2/7
So, to summarize:
Question A: You need to draw a Venn Diagram.
Question B: The probability of having a sandwich but not fruit is 1/10.
Question C: The probability of having fruit given that they have salad is 2/7.