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Chapter 11and 12 Review Math 303B
Section 11.1
1. For any event A, 0
.

P
(
A
)1

A) True
B) False
2. An outcome is one of the possible things that can occur in a probability experiment.
A) True
B) False
3. Which of the following is an event for the experiment "tossing a pair of dice"?
A) 
(
1
,
2
)
,
(
2
,
3
)
,
(
4
,
5
)

B) 
(
1
,7
)
,(
2
,
1
)

C)
D)
(
2
,3
,
1
)
,(
1
,
5
)


(
1
,
4
)
,
(
3
,
4
)
,
(
1
)


4. If a coin is tossed 112 times, then the greatest number of times a head could possibly
occur is
A) 56
B) 28
C) 112
D) None of the other choices.
5. A bag contains some colored balls, some red, some blue, and some green. If P(red) =
1 and P(blue) = 1 , determine P(green). Write your answer as a fraction.
3
5
6. If P(A) = 1 , P(B) = 1 , and A
, then P( A
) = __________. (Write your

B



B
6
7
answer as a fraction.)
7. If P(A) = 7 , then P
(A
) _________. (Write your answer as a fraction.)
8
8. An experiment was performed 144 times. Let A be a particular event. What is the
smallest possible value which n(A) could have?
A) 72
B) 36
C) 0
D) None of the other choices.
9. An experiment was performed 100 times. Let A be a particular event. What is the
largest possible value which n(A) could have?
A 100
B) 99
C) 50
D) None of the other choices.
10. An experiment was performed 120 times. Let A be a particular event. What is the
smallest possible value the relative frequency of event A could have?
A) 1
B)
2
1
120
C) 0
D) None of the other choices.
11. A weather report indicates that there is a 20%
chance of rain in Lancaster County
tomorrow morning. Which is a correct interpretation?
A) It will rain for 4.8hours of the next 24 hours.
B) It will rain on 20%
of the area of Lancaster County.
C) Of past days when conditions were similar, 1 out of 5 of them had some rain.
D) None of the other choices.
12. An 8-sided die is rolled 130 times with the following results recorded:
Outcome
Frequency
25
1
3
2
13
3
15
4
0
5
15
6
7
11
48
8
One can conclude from this experiment that it is not possible to roll a 5 using this die.
A) True
B) False
13. An 8-sided die is rolled 110 times with the following results recorded:
Outcome
Frequency
23
1
2
1
15
3
10
4
0
5
6
14
13
7
34
8
Find the experimental probability of getting either a 1 or 3 on a single roll.
A) 19
55
B) 38
C) 0.38
D) None of the other choices.
14. An 8-sided die is rolled 107times with the following results recorded:
Outcome
Frequency
1
22
2
2
15
3
4
14
0
5
10
6
13
7
31
8
Find the experimental probability of getting an even number on a single roll.
A) 57
107
B) 57
C) 56
107
D) None of the other choices.
15. A card is drawn from a standard 52-card deck. Which of the following are true?
(i) P(getting a red card or getting a queen) = 7 13
(ii) P(getting a 5 or getting a red 6 ) = 113
(iii) P(getting an ace or a spade) = 4 13
A) (i) and (ii) only
B) (i) and (iii) only
C) (ii) and (iii) only
D) (i), (ii), and (iii)
16. A card is drawn from a standard 52-card deck. Let A be the event "you draw either a
9 or a red 8 ." Compute PA
( ). (Write your answer as a fraction.)
17. P
A

B

P
A

P
B

P
A

B
, for any two events A and B.






A) True
B) False
18. How many elements are in the sample space of the experiment "toss 2 dice and flip a
coin?"
A) 3
B) 18
C) 72
D) None of A, B, or C
19. How do we compute the probability of an event A with equally likely outcomes?
Use the following to answer questions 20-22:
A spinner with five equally sized and shaped sectors is spun once.
2
1
5
3
4
nA
()
nA
()
, PA
PA
( )
( )
nS
()
nS
()
20. What is the probability the spinner lands on 3, 4, or 5?
A) 1
5
B) 2
5
C) 3
5
D) 4
5
21. What is the probability the spinner lands on a number less than 3?
A) 1
5
B) 2
5
C) 3
5
D) 4
5
22. What is the probability the spinner lands on 3?
A) 1
5
B) 2
5
C) 3
5
D) 4
5
23. A box contains five blue, eight green, and three yellow balls. If a ball is selected at
random, what is the probability that it is green?
A

B
0
24. True or False. If the events A and B are mutually exclusive, then P
.


25. What is the sample space of the experiment consisting of rolling two indistinguishable foursided dice, each of which has sides marked as A, B, C, and D?
Section 11.2
1. Two dice are thrown. If each face is equally likely to turn up, find the probability that
the sum is at least 7. (Write your answer as a fraction.)
2. In tossing two fair dice, the probability of getting a sum that is a divisor of 12 is 17 .
36
A) True
B) False
3. A certain jukebox contains only three classic CDs: Deep Purple, ABBA, and Def
Leopard. If the probability that Deep Purple is playing is 1 5 and the probability that
ABBA is playing is 1 6 , what is the probablity that Def Leopard is playing?
A) 19
30
B)
1
C)
1
5
6
D) None of the other choices
4.
5. A container contains 2 red, 3 white, and 5 yellow balls. Suppose that once a ball is
drawn it is not replaced. What is the probability that 2 red balls will be drawn in 2
tries? (Express your answer as a fraction.)
6. Find the probability P(prime sum when tossing 2 dice). (Write your answer as a
fraction.)
7. How many different single-scoop ice cream cones can you make if there are 3 types of
cones, 4 sizes of each cone, and 30 flavors?
8.
9. A circular game spinner is comprised of 5 different colors, each of which takes up the
following amount of space in terms of its central angle:
Color
Red
Central Angle
Yellow
40
Blue
40
Green
80
White
170
30
P(red spin) = _______________
A) 30
B) 1
12
C)
1
6
D) None of the other choices
10. The numbers in the row of Pascal's triangle corresponding to 5 tosses of a coin must
sum to 32 .
A) True
B) False
11, 12, 13, 14, 15, 16, 17
18. Explain the difference between experimental probability and theoretical probability.
19. Suppose S = {e1, e2, e3, e4, e5} for some experiment, and P(e1) = 0. 3 , P(e2) = 0. 2 , P(e3)
= 0.0 1 , P(e4) = 0. 11 . Find P(e5). (Express your answer accurate to two decimal places.)
20. 21, 22
23. A circular game spinner is comprised of 5 different colors, each of which takes up the
following amount of space in terms of its central angle:
Color
Red
Central Angle
Yellow
40
Blue
40
Green
80
White
170
30
You spin the spinner twice and record the results.
P(2 red spins) = _______________
A) 60
B) 1/144
C) 1/36
D) None of the other choices
24. True or False? For any two events A and B, P
.
(
A

B
)

P
(
A
)

P
(
B
)
Section 12.1
1. Every kite is a rhombus, but not every rhombus is a kite.
A) True
B) False
2. Every square is a rectangle, but not every rectangle is a square.
A) True
B) False
3. Which of the following is(are) true about this figure on the square lattice?
(i) It is a parallelogram.
(ii) It is a kite.
A) (i) only
B) (ii) only
C) Both (i) and (ii)
D) Neither (i) nor (ii)
4. Which of the following types of polygons do not exist?
(i) E
right triangles
q
u
i
l
a
t
e
r
a
l
(ii) T
with right angles
r
a
p
e
z
o
i
d
s
h
o
m
b
iwith all acute angles
(iii) R
A) (i) and (ii) only
B) (i) and (iii) only
C) (ii) and (iii) only
D) None of the other choices
5. Which of the following is(are) true about the figure on the square lattice below?
(i) It is a parallelogram.
(ii) It is a kite.
A) (i) only
B) (ii) only
C) Both (i) and (ii)
D) Neither (i) nor (ii)
6. Determine the properties of the triangle shown on the square lattice below. List all of
the following properties that apply, separated by semicolons:
acute, equilateral, isosceles, obtuse, right, scalene
7. A kitecan be both equiangular and equilateral.
A) True
B) False
8. Determine the number of s
in the following square lattice.
q
u
a
r
e
s
9. Determine the number of e
triangles in the following square lattice:
q
u
i
a
n
g
u
l
a
r
10. Which of the following is(are) true?
(i) There does not exist a scalene e
q
u
i
l
a
t
e
r
a
ltriangle.
(ii) A right triangle cannot be scalene.
(iii) An equilateral triangle is necessarily equiangular.
A) (iii) only
B) (i) only
C) (i) and (iii) only
D) (i), (ii), and (iii)
Use the following to answer questions 11-14
The diagram below is drawn on a square lattice.
A
E
G
H
B
M
N
I
C
D
K
J
L
O
11. The quadrilaterals E
G
H
B
K
J, and L
N
M
K
, IH
are all squares.
A) True
B) False
12. Which of the following are accurate descriptors for the triangle ACO?
(i) right
(ii) scalene
(iii) equilateral
(iv) isosceles
A) (i) and (ii) only
B) (i) and (iii) only
C) (i) and (iv) only
D) None of the other choices
13. The quadrilateral B
E
G
H
is a rhombus, but not a square.
A) True
B) False
14. Which of the following are true?
N
Ois an isosceles right triangle.
(i) L
K
JI is a parallelogram.
(ii) H
(iii) There are no kites in the figure.
A) (i) and (iii) only
B) (i) and (ii) only
C) (ii) and (iii) only
D) (ii) only
15. A r
can be drawn on a triangular lattice.
e
c
t
a
n
g
l
e
A) True
B) False
Use the following to answer questions 16-19
The diagram below is drawn on a triangular lattice.
B
A
E
N
O
M
G
D
I
C
K
H
J
F
16. Which of the following is(are) true?
B
C
D
(i) A
is a square.
G
H
(ii) B
is an e
triangle.
q
u
i
a
n
g
u
l
a
r
H
JIis a rhombus.
(iii) M
A) (i) and (iii) only
B) (ii) and (iii) only
C) (i) and (ii) only
D) (ii) only
17. B
G
H
is a right triangle.
A) True
B) False
18. G
M
K
is a right scalene triangle.
A) True
B) False
19. Find all rhombi in the diagram. List your answers separated by semicolons.
20. Which of the following types of polygons, if any, do not exist?
(i) Equilateral right triangles
(ii) Trapezoids with right angles
(iii) Kites with all acute angles
A) (i) and (ii) only
B) (i) and (iii) only
C) (ii) and (iii) only
D) None of A, B, or C
21. Which of the following types of polygons do not exist?
(i) Parallelograms with right angles
(ii) Kites with all obtuse angles
(iii) Trapezoids with all acute angles
A) (i) and (ii) only
B) (i) and (iii) only
C) (ii) and (iii) only
D) (i), (ii), and (iii)
22. The Van Hiele Theory identifies four levels through which learning geometry
progresses.
A) True
B) False
Section 12.2
1. A r
h
o
m
b
u
shas rotation symmetry.
A) True
B) False
2. A s
q
u
a
r
ehas reflection symmetry.
A) True
B) False
3.
4. Which of the following shapes always have rotation symmetry (through less than a full
turn)?
(i) parallelogram
(ii) s
q
u
a
r
e
(iii) i
s
o
s
c
e
l
e
s
t
r
a
p
e
z
o
i
d
A) (i) and (ii) only
B) (ii) only
C) (ii) and (iii) only
D) None of the other choices.
5, 6, 7
8. There exist shapes which possess reflection symmetry but not rotation symmetry, and
vice versa.
A) True
B) False
9. Which of the following is(are) true?
(i) The diagonals of a r
bisect each other.
e
c
t
a
n
g
l
e
(ii) The diagonals of a p
bisect opposite angles.
a
r
a
l
l
e
l
o
g
r
a
m
(iii) The diagonals of a r
may not be perpendicular.
h
o
m
b
u
s
A) (i) only
B) (ii) only
C) (i) and (ii) only
D) (i), (ii), and (iii)
10. Which of the following are true?
(i) Both pairs of opposite sides are not necessarily congruent in a r
.
e
c
t
a
n
g
l
e
(ii) Adjacent sides of a p
can be perpendicular.
a
r
a
l
l
e
l
o
g
r
a
m
(iii) All angles in a s
are congruent.
q
u
a
r
e
A) (i) and (ii) only
B) (i) and (iii) only
C) (ii) and (iii) only
D) (i), (ii), and (iii)
11. A p
must have either reflection symmetry or rotation symmetry.
a
r
a
l
l
e
l
o
g
r
a
m
A) True
B) False
12. Which of the following types of symmetry does a circle possess?
A) reflection
B) rotation
C) Both A and B
D) Neither A nor B
13, 14, 15
16. The following shape satisfies which conditions?
S: simple closed curve
C: convex, simple closed curve
N: n-gon
A)
B)
C)
D)
S only
S and C only
S and N only
S, C, and N
17. Any reflection line of a circle must pass through the center of the circle.
A) True
B) False
18. A semicircle is a simple, closed curve.
A) True
B) False
19. The region bounded by a quadrilateral must be convex.
A) True
B) False
20. The number of exterior angles in a regular n-gon is _______ the number of interior
angles.
A) equal to
B) twice
C) half
D) three times
.
Section 12.3
1. An equilateral triangle can have a right angle.
A) True
B) False
2.
3. Any triangle has at most two acute angles.
A) True
B) False
4. Which of the following types of polygons do not exist?
(i) P
with right angles
a
r
a
l
l
e
l
o
g
r
a
m
s
(ii) I
with all obtuse angles
s
o
s
c
e
l
e
s
t
r
a
p
e
z
o
i
d
s
(iii) Q
with all acute angles
u
a
d
r
i
l
a
t
e
r
a
l
s
A) (i) and (ii) only
B) (i) and (iii) only
C) (ii) and (iii) only
D) None of the other choices
5. Consider the following diagram. Which statement, if either, is true?
(i) m4 + m5 + m6 = 180°
(ii) m7 + m8 + m9 = 360°
A) (i) only
B) (ii) only
C) Both (i) and (ii)
D) Neither (i) nor (ii)
6. In the following diagram m2 = 90°. Which statement, if either, is true?
(i) Angles 1
are complementary.
a
n
d
3
(ii) Angles 1
are complementary.
a
n
d
6
A) (i) only
B) (ii) only
C) Both (i) and (ii)
D) Neither (i) nor (ii)
7. Given that "a + b + c = 180°", one can conclude that d + e + f = _____ °.
Use the following to answer questions 8-9:
The following diagram is drawn on a square lattice.
8. Fill in the blanks with the appropriate segments: AB || ______ and BC || _______ .
(List your answers separated by a semicolon.)
9. Which line segment is perpendicular to FG ?
10. Which of the following are true?
(i) 76° is an acute angle.
(ii) 180.43° is a reflex angle.
(iii) The complement of 13° is an acute angle.
A) (i) and (ii) only
B) (i) and (iii) only
C) (ii) and (iii) only
D) (i), (ii), and (iii)
11. Given the following diagram, line l must be parallel to line m.
l
m
x
x
t
A) True
B) False
12. Two v
.
e
r
t
i
c
a
langles can be s
u
p
p
l
e
m
e
n
t
a
r
y
A) True
B) False
13. The measure of A is 12° more than three times the measure of B. If A and B are
supplementary angles, find the measure of A.
A) 137°
B) 138°
C) 139°
D) 140°
14. The measure of Xis 40 less than 9 times the measure of Y. If Xand Y are
complementary angles, find the measure of Y.
15. Find the missing angle measure.
4
9

2
7

Use the following to answer questions 16-20
In the following figure, line l is parallel to line m, and the measure of 3 is 92°.
1 2
4 3
5 6
7 8
l
m
16. Find the measure of 2.
17. Find the measure of 1.
18. Find the measure of 8.
19. Find the measure of 5.
20. Find the measure of 7.
21. True or False? 3 and 7 are supplementary angles.
Section 12.4
4. If the measure of the exterior angles of a regular polygon is 60 , how many sides does
the polygon have?
5. The angle sum in a regular 5 -gon is _______.
A) 180 5
B) 180 4
C) 180 3
D) None of the other choices
6. The measure of a vertex angle in a regular 15 -gon is ________.
A) 13
180
15
B) 15
180
13
C) 13
360
15
D) 15
360
13
7. The measure of an exterior angle in a regular 11 -gon is _______.
A) 3 6 0
9
B) 3 6 0
11
C) 1 8 0
9
D) 1 8 0
11
8. The measure of a central angle in a regular 15 -gon is _______.
A) 3 6 0
13
B) 3 6 0
15
C) 1 8 0
13
D) 1 8 0
15
9, 10.
11. The measures of the vertex angles in a given quadrilateral are
xxx
,
8
,

8
,
a
n
d
8
. Determine the measures of all angles. (Write the angles




separated by semicolons.)
12. Four of the five vertex angles of a pentagon have measures 1
.
6
0
,
4
5
,
4
4
,
a
n
d
7
7
Find the measure of the fifth vertex angle.
Use the following to answer questions 13-14:
B
x
2x C
y
30
A
z
D
13. Determine the measure of 
.
A
C
B
14. Determine the measure of 
.
D
A
C
15. The sum of the measures of the vertex angles of a regular polygon is 900 . How many
sides does the polygon have?
A) 6
B) 7
C) 4
D) None of the other choices
19. The central angle of a regular 18 -gon measures ____________.
A) 20
B) 10
C) 90
D) None of the other choices
20. Find the measures of the vertex angles for a regular 6 -gon. Round to the nearest tenth
of a degree, if necessary.
Section 12.5
1. A cube has 6 faces, 8 vertices, and 13 edges.
A) True
B) False
2
3. If the lateral faces of a prism are s
, then the prism is a right prism.
q
u
a
r
e
s
A) True
B) False
8, 9.
Use the following to answer questions 10-15:
10. Name the bases of the prism.
11. Name the lateral faces of the prism.
12. Name the faces that are hidden from view.
13. Name the prism by type.
14. Fill in the table for the prism.
Number of Faces
F
Number of vertices
V
Number of Edges
F+V
15. Does this prism satisfy Euler's formula?
A) Yes
B) No
16.
17. Determine whether the following are polyhedra.
(i)
(ii)
A) (i) polyhedron
(ii) polyhedron
B) (i) not a polyhedron (ii) not a polyhedron
(ii) not a polyhedron
C) (i) polyhedron
D) (i) not a polyhedron (ii) polyhedron
E
18. The shape below is a regular polyhedron.
A) True
B) False