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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Your Venn diagram entries appear correct and are consistent with the 30 students
B) is correct
C) This a conditional probability
P(A | B) ---> read: the probability of A given B
= P(A and B)/P(B)
for yours:
P(Fruit | Salad)
= P(Fruit and Salad)/P(salad)
= (7/30) / (18/30)
= 7/18
Thank you Reiny
To solve Question A, we need to draw a Venn diagram to represent the given information. The Venn diagram consists of three circles: one for sandwiches, one for salads, and one for fruit.
According to the information provided:
- There are 5 students who had a sandwich, salad, and fruit (this number goes in the intersection of all three circles).
- There are 3 students who had a sandwich only (this number goes in the section of the sandwich circle that does not overlap with the other two circles).
- There are 7 students who had salad only (this number goes in the section of the salad circle that does not overlap with the other two circles).
- There are 7 students who had fruit only (this number goes in the section of the fruit circle that does not overlap with the other two circles).
- There are 4 students who had a sandwich and salad (this number goes in the overlapping region between the sandwich and salad circles).
- There are 2 students who had a sandwich and fruit (this number goes in the overlapping region between the sandwich and fruit circles).
- There are 2 students who had salad and fruit (this number goes in the overlapping region between the salad and fruit circles).
To solve Question B, we are asked to find the probability that a randomly chosen person has a sandwich but not fruit. In the Venn diagram, this corresponds to the number of students in the sandwich circle except for the overlapping region with the fruit circle.
By adding up the numbers, we have 3 + 4 + 2 = 9 students who have a sandwich (including those who have it with salad or fruit). But since we want to exclude the students who also have fruit, we subtract the number in the overlapping region, which is 2.
So, the number of students with a sandwich but not fruit is 9 - 2 = 7. The total number of students surveyed is given as 30, so the probability is 7/30.
The answer to Question B is 7/30.
To solve Question C, we are asked to find the probability that a randomly chosen person, given that they have salad, also has fruit. In the Venn diagram, this corresponds to the number of students in the overlapping region between the salad and fruit circles divided by the total number of students who have salad.
From the Venn diagram, we can see that there are 2 students in the overlapping region between the salad and fruit circles. The total number of students who have salad, as stated in the information, is 7.
So, the probability is 2/7.
The answer to Question C is 2/7.