MA 110
EVEN MORE THREE CIRCLE VENN DIAGRAMS
1.
A merchant surveyed 400 people to determine the way they learned about an upcoming
sale. The survey showed that 180 learned about the sale from the radio, 190 from
television, 190 from the newspaper, 80 from radio and television, 90 from the radio and
newspaper, 50 from television and newspaper, and 30 from all three sources.
A.
Draw a three-circle Venn diagram using the data above.
80 - 30
R
T
40
190 – (50 + 30 + 20)
90
50
50 - 30
30
180 – (50 + 30 + 60)
60
20
90 - 30
80
N
B.
190 – (60 + 30 + 20)
30
400 – (all circle totals)
How many people learned of the sale from only one of the three sources?
40 + 80 + 90 = 210
C.
How many people learned of the sale from newspapers or radios but not both?
80 + 20 + 50 + 40= 190
D.
How many people learned of the sale only from newspapers?
80
E.
How many people learned of the sale from the radio or the television (or both)?
40 + 50 + 90 + 60 + 30 + 20 = 290
110 W SECTION 7-2 EVEN MORE VENN DIAGRAMS solutions
PAGE: 1 OF 2
2.
One hundred students were asked if they liked listening to pop, rap, or country music.
Thirty-two students like rap music. Ten students liked pop and rap music, but only one
of them liked all three kinds of music. Twenty-four students said they liked pop and
country music. Thirty students like only pop music. Nine students like rap and country,
but not pop music. Four students said they did not like any of the three types of music.
A.
Draw a three-circle Venn diagram using the data above.
P
R
9
13
30
10 liked pop and
rock, but 1 likes all 3.
1
9
23
9 like rap and
country, but not pop.
11
4
24 – 1
C
B.
How many students like only country music?
100 – (30 + 9 + 13 +
23 + 1 + 9 + 4)
11
C.
How many students like pop and country, but not rap music?
23
D.
How many students do not like rap music?
30 + 23 + 11 + 4 = 68
E.
How many students either like country music or do not like rap music?
23 + 1 + 9 + 11 + 30 + 4 = 78
F.
How many students like only one style of music?
30 + 13 + 11 = 54
G.
How many students like at least one style of music?
100 – 4 = 96
110 W SECTION 7-2 EVEN MORE VENN DIAGRAMS solutions
PAGE: 2 OF 2