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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Agree with B.
B. How many had salad? 18
Of those, how many also had fruit?
7 So it is 7/18
To answer Question A, let's draw a Venn Diagram to represent the information given. Start by drawing two overlapping circles to represent the categories: sandwich and salad. Then, label the regions as follows:
- The region where the two circles overlap represents the students who had a sandwich, salad, and fruit (5 students).
- The region of the sandwich-only circle that is not overlapping represents the students who had a sandwich only (3 students).
- The region of the salad-only circle that is not overlapping represents the students who had a salad only (7 students).
- The rest of the regions represent the students who had fruit only (7 students), a sandwich and salad (4 students), a sandwich and fruit (2 students), and salad and fruit (2 students).
Now, let's move on to Question B. We want to find the probability that a randomly chosen person has a sandwich but not fruit.
To do this, we need to find the number of people who have a sandwich but not fruit, which is represented by the sandwich-only region (3 students). The total number of students is given as 30.
Therefore, the probability is calculated as:
number of people with a sandwich but not fruit / total number of students = 3/30 = 1/10
So, the probability that they have a sandwich but not fruit is 1/10.
Moving on to Question C, we are given that the person has salad and we need to find the probability that they also have fruit.
To start, we need to find the number of people who have salad (7 students). Then, we look at the subset of these students who also have fruit, represented by the salad and fruit region (2 students).
Therefore, the probability is calculated as:
number of people with salad and fruit / number of people with salad = 2/7
So, the probability that a person who has salad also has fruit is 2/7.