Question 1207215: A music teacher has surveyed 500 students. The results of the survey are as follows: 221 students like rap music, 209 students like rock music; 229 students like heavy metal music; 83 students like both rap music and rock music: 92 students like both rap music and heavy metal music; 99 students like both rock music and heavy metal music; 38 students like all three, Construct a Venn diagram representing the given information and answer the following. How many of these students like:
1. exactly three types of music!
2. only rock music?
3. rock music or heavy metal music?
4. none of the mentioned types of music?
5. only one of the given types of music?
6. rap music and rock music, but not heavy metal?
7. at least one of the given types of music?
8. heavy metal or rock music, but not rap music?
9. heavy metal music?
10. only rap music?
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
You don't get any benefit from this if we show you the whole solution....
You draw the diagram with the three intersecting circles; then I will explain how to do the work to allow you to answer the given questions.
Some shorthand for my discussion....
A = rap
B = rock
C = heavy metal
Then, for example...
"ABC" is the number of students who like all three types of music
"AC" is the number who like rap and heavy metal but not rock
"B" is the number who like only rock
(1) ABC = 38 (given)
(2) 83 like both rap and rock. Since 38 students like all three types of music, the number who like rap and rock but not heavy metal is 83-38 = 45:
AB = 45
Use similar calculations to find AC (number who like rap and heavy metal but not rock) and BC (number who like rock and heavy metal but not rap).
(3) "A" is the number of students who like only rap. A total of 221 like rap; of those, "AB" like both rap and rock, "AC" like both rap and heavy metal, and "ABC" like all three. So "A", the number who like only rap, is the total number who like rap, minus the numbers who like both rap and any of the other types:
A = 221 - (AB+AC+ABC)
Use similar calculations to find "B" and "C" -- those who like only rock, or only heavy metal.
(4) You now have "A", "B", and "C" -- numbers who like only one of the three types; "AB", "AC", and "BC" -- numbers who like two of the three types; and "ABC" (given) -- the number who like all three types. The number who like none of the three types is the total number of students (500), minus the sum of all those numbers:
500 - (A+B+C+AB+AC+BC+ABC)
All the sections of your Venn diagram now have the numbers you need to answer the questions.
Answer by ikleyn(52794)  (Show Source):
You can put this solution on YOUR website! .
When a post comes with 10 questions, for me this is a sure sign that the visitor
who sent this post does not want to know anything at all and does not want
to learn anything. His/her goal is not knowledge and is not learning.
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