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?
16
Question 2: How many liked the Little Mermaid but NOT Mickey Mouse?
29
Question 3: How many students did NOT like Mickey Mouse?
41
Am I correct with this??
#1 24
#2 46
#3 70
How are you getting 24, 46, and 70?
I did a venn diagram and I got 16, 29 and 41?/
To answer these questions, we can use the principle of inclusion-exclusion.
Question 1: To find the number of students who liked ONLY 101 Dalmatians, you need to subtract the number of students who liked both The Little Mermaid and 101 Dalmatians, and those who liked all three movies, from the total number of students who liked 101 Dalmatians.
Total number of students who liked 101 Dalmatians = 43
Number of students who liked both The Little Mermaid and 101 Dalmatians = 7
Number of students who liked all three movies = 4
Subtracting the two from the total, we get:
43 - 7 - 4 = 32
Therefore, the correct answer to Question 1 is 32, not 16.
Question 2: To find the number of students who liked The Little Mermaid but NOT Mickey Mouse, you need to subtract the number of students who liked both The Little Mermaid and Mickey Mouse, and those who liked all three movies, from the total number of students who liked The Little Mermaid.
Total number of students who liked The Little Mermaid = 39
Number of students who liked both The Little Mermaid and Mickey Mouse = 10
Number of students who liked all three movies = 4
Subtracting the two from the total, we get:
39 - 10 - 4 = 25
Therefore, the correct answer to Question 2 is 25, not 29.
Question 3: To find the number of students who did NOT like Mickey Mouse, we need to find the complement, which is the total number of students minus the number of students who liked Mickey Mouse.
Total number of students = 115
Number of students who liked Mickey Mouse = 56
115 - 56 = 59
Therefore, the correct answer to Question 3 is 59, not 41.
So, your answers are not correct.