7.3 Check Yourself
Use the Venn diagram below to find the number of elements in the region.
1) n(A)
2) n(A
1)
2)
B)
3) n(C )
3)
4) n(A
C)
5) n(A
B
6) n((A
B)
4)
5)
C)
6)
C)
Use the addition principle for counting to solve the problem.
7) If n(A) = 5, n(B) = 11 and n(A B) = 3, what is n(A B)?
8) If n(A) = 40, n(B) = 117 and n(A
9) If n(B) = 24, n(A
10) If n(A) = 20, n(A
B) = 137, what is n(A
B) =5, and n(A
B) = 58, and n(A
7)
B)?
B) = 42, find n(A).
B) = 16, find n(B).
Provide an appropriate response.
11) Results of a survey of fifty students indicate that 30 like red jelly beans,
29 like green jelly beans, and 17 like both red and green jelly beans. How
many of the students surveyed like only green jelly beans?
12) Mrs. Bollo's second grade class of thirty students conducted a pet
ownership survey. Results of the survey indicate that 8 students own a
cat, 15 students own a dog, and 5 students own both a cat and a dog.
How many of the students surveyed own neither a cat nor a dog?
1
8)
9)
10)
11)
12)
13) A survey of residents in a certain town indicates 170 own a
dehumidifier, 130 own a snow blower, and 80 own a dehumidifier and a
snow blower. How many own a dehumidifier or a snow blower?
13)
14) A local television station sends out questionnaires to determine if
viewers would rather see a documentary, an interview show, or reruns
of a game show. There were 900 responses with the following results:
14)
270 were interested in an interview show and a documentary, but not
reruns.
36 were interested in an interview show and reruns but not a
documentary
126 were interested in reruns but not an interview show.
216 were interested in an interview show but not a documentary.
90 were interested in a documentary and reruns.
54 were interested in an interview show and reruns.
72 were interested in none of the three.
How many are interested in exactly one kind of show?
15) In a group of 42 students, 22 take history, 17 take biology and 8 take
both history and biology.
How many students take biology, but not history?
15)
16) In a group of 42 students, 22 take history, 17 take biology and 8 take
both history and biology.
How many students take neither biology nor history?
16)
17) Suppose there are 4 trains connecting town X to town Y and 6 roads
connecting town Y to town Z. In how many ways can a person travel
from X to Z via Y?
17)
18) A Super Duper Jean company has 3 designs that can be made with short
or long length. There are 5 color patterns available. How many different
types of jeans are available from this company?
18)
19) A restaurant offered pizza with 3 types of crusts and 7 different
toppings. How many different types of pizzas could be offered?
19)
20) How many different sequences of 4 digits are possible if the first digit
must be 3, 4, or 5 and if the sequence may not end in 000? Repetition of
digits is allowed.
20)
2
Answer Key
Testname: 7.3 CHECK YOURSELF
17
2) 29
3) 24
4) 10
5) 8
6) 15
7) 13
8) 20
9) 23
10) 54
11) 12
12) 12
13) 220
14) 432
15) 9
16) 11
17) 24
18) 30
19) 21
20) 2997
1)
3