What is a Venn diagram good for?
I’m trying to use one for this problem
A study was made of 200 preschoolers to determine if they watched some particular television shows. The choices were Little Galileo, Super Reader and Prehistoric Train. The results are
I. 22 preschoolers did not watch any of these shows
II. 73 preschoolers only watched Little Galileo
III. 136 preschoolers watched Little Galileo
IV. 14 preschoolers only watched Super Reader and Prehistoric Train
V. 31 preschoolers only watched Little Galileo and Prehistoric Train
VI. 63 preschoolers watch Super Reader
VII. 135 preschoolers do not watch Prehistoric TraiHow many students are in the event Watches Little Galileo and Super Reader?
A Venn diagram is a useful tool for visually representing relationships between different sets or groups of objects. It consists of overlapping circles or shapes that represent different categories, with the overlapping regions indicating where the categories intersect.
In the given problem, we are interested in finding the number of students who watch Little Galileo and Super Reader. To solve this, we can use the following steps:
Step 1: Draw a Venn diagram with two circles representing Little Galileo and Super Reader.
Step 2: Label the regions of the Venn diagram with the given information:
- The number of preschoolers who only watch Little Galileo is 73, so this goes in the region that is exclusive to Little Galileo.
- The number of preschoolers who watch both Little Galileo and Prehistoric Train is 31, so this goes in the overlapping region between Little Galileo and Prehistoric Train.
- The number of preschoolers who watch Super Reader is 63, so this goes in the region that is exclusive to Super Reader.
Step 3: Use the information from the Venn diagram to determine the number of students who watch both Little Galileo and Super Reader:
- From the Venn diagram, we can see that the number of students in the overlapping region between Little Galileo and Super Reader is 0. This means that there are no students who watch both Little Galileo and Super Reader.
Thus, the answer to the question "How many students are in the event Watches Little Galileo and Super Reader?" is 0.
To find the answer to the question, "How many students are in the event Watches Little Galileo and Super Reader?", we can make use of a Venn diagram.
A Venn diagram is a visual representation of the relationships between different sets or groups. It consists of overlapping circles or other shapes that represent the sets, and the overlapping regions represent the elements or items that belong to multiple sets.
In this case, we have three sets: Little Galileo watchers, Super Reader watchers, and Prehistoric Train watchers.
To organize the given information, we can start by drawing two overlapping circles: one to represent Little Galileo watchers and the other to represent Super Reader watchers. We then fill in the information provided by the statements IV, V, and VI:
- 14 preschoolers only watched Super Reader and Prehistoric Train: This means that the intersection of Super Reader watchers and Prehistoric Train watchers has 14 elements.
- 31 preschoolers only watched Little Galileo and Prehistoric Train: This means that the intersection of Little Galileo watchers and Prehistoric Train watchers has 31 elements.
- 63 preschoolers watch Super Reader: This means that the number of Super Reader watchers is 63.
Next, we can use the other given information to complete the Venn diagram:
- 22 preschoolers did not watch any of these shows: This means that the region outside of all three circles has 22 elements.
- 73 preschoolers only watched Little Galileo: This means that the region inside the Little Galileo circle but outside the other circles has 73 elements.
- 136 preschoolers watched Little Galileo: Since we have already accounted for the 73 who only watched Little Galileo, the remaining 63 elements must be in the intersection of Little Galileo watchers and Super Reader watchers.
- 135 preschoolers do not watch Prehistoric Train: This means that the region outside the Prehistoric Train circle has 135 elements.
Now we can determine the number of students in the event "Watches Little Galileo and Super Reader" by looking at the intersection of the Little Galileo and Super Reader circles. We see that this intersection is represented by the 63 elements mentioned earlier.
Therefore, the answer to the question is that 63 students are in the event "Watches Little Galileo and Super Reader".
See
https://www.jiskha.com/questions/1786542/A-study-was-made-of-200-preschoolers-to-determine-if-they-watched-some-particular
Venn diagrams help to visualize the various subsets of the population.
google is your friend, for examples.
Surely your text has illustrations.
Once you have identified the various unknowns, you can solve algebraically. Then you can answer any questions about probabilities and so forth