I need help with these questions:
A survey of 115 children found that
39 liked The Little Mermaid
43 liked 101 Dalmatians
56 liked Mickey Mouse
7 liked The Little Mermaid and 101 Dalmatians
10 liked The Little Mermaid and Mickey Mouse
16 liked 101 Dalmatians and Mickey Mouse
4 liked all three
Question 1: How many students liked ONLY 101 Dalmatians?
Question 2: How many liked the Little Mermaid but NOT Mickey Mouse?
Question 3: How many students did NOT like Mickey Mouse?
**How do I solve this??
Did you make a Venn diagram yet? Put any numbers in it?
Start with the 4 in the middle.
Then work your way out from there.
Ok I think I might understand it now.
1. 16
2. 29
3. 41
Am I correct?
Thanks!
To solve these questions, we can use a Venn diagram and the concept of set theory.
Step 1: Draw a Venn diagram with three overlapping circles representing The Little Mermaid (LM), 101 Dalmatians (101D), and Mickey Mouse (MM).
Step 2: Start filling in the information given in the problem.
- Out of 115 children surveyed, 39 liked The Little Mermaid (LM), so mark 39 in the LM circle.
- 43 children liked 101 Dalmatians (101D), so mark 43 in the 101D circle.
- 56 children liked Mickey Mouse (MM), so mark 56 in the MM circle.
- 7 children liked both The Little Mermaid and 101 Dalmatians, so mark 7 in the overlapping region between LM and 101D.
- 10 children liked The Little Mermaid and Mickey Mouse, so mark 10 in the overlapping region between LM and MM.
- 16 children liked both 101 Dalmatians and Mickey Mouse, so mark 16 in the overlapping region between 101D and MM.
- 4 children liked all three movies, so mark 4 in the region where all three circles overlap.
Step 3: Use the Venn diagram to answer the questions.
Question 1: How many students liked ONLY 101 Dalmatians?
To find the number of students who liked ONLY 101 Dalmatians, we need to exclude the children who liked both other movies. From the Venn diagram, we can see that the number of students who liked ONLY 101 Dalmatians is the difference between the number of students who liked 101 Dalmatians (43) and those who liked both 101 Dalmatians and the other two movies (7 and 16). Therefore, the number of students who liked ONLY 101 Dalmatians is 43 - 7 - 16 = 20.
Question 2: How many liked the Little Mermaid but NOT Mickey Mouse?
Using the Venn diagram, we can see that the number of students who liked The Little Mermaid but not Mickey Mouse is the difference between the number of students who liked The Little Mermaid (39) and those who liked both The Little Mermaid and Mickey Mouse (10) and those who liked all three movies (4). Therefore, the number of students who liked The Little Mermaid but not Mickey Mouse is 39 - 10 - 4 = 25.
Question 3: How many students did NOT like Mickey Mouse?
To find the number of students who did not like Mickey Mouse, we need to exclude the children who liked Mickey Mouse. From the Venn diagram, we can see that the number of students who did not like Mickey Mouse is the sum of those who liked only The Little Mermaid, only 101 Dalmatians, and those who did not like any of the movies. Therefore, the number of students who did not like Mickey Mouse is (39 - 10 - 4) + (43 - 7 - 16) + (115 - 39 - 43 - 56 + 7 + 10 + 16 + 4) = 16.