CCSSREASONING
Point X is chosen at
random on
. Find the probability of each
event.
6.
P(X is on )
SOLUTION:
ANSWER:
, 0.44, or 44%
8.
P(X is on )
SOLUTION:
ANSWER:
, 0.56, or 56%
10.
BIRDS
Four birds are sitting on a telephone wire.
What is the probability that a fifth bird landing at a
randomly selected point on the wire will sit at some
point between birds 3 and 4?
SOLUTION:
ANSWER:
, 0.33, or 33%
Find the probability that a point chosen at
random lies in the shaded region.
12.
SOLUTION:
ANSWER:
, 0.375 or 37.5%
14.
SOLUTION:
If a region A contains a region B and a point E in
region A is chosen at random, then the probability
that point E is in region B is
The area of a regular polygon is the half the product
of the apothem and the perimeter. Find the apothem.
The length of the apothem of an hexagon of side
length a units is
Area of the large hexagon:
Area of the small hexagons:

The area of the shaded region is
.
Therefore, the probability is
ANSWER:
, 0.4375, or 43.75%
Use the spinner to find each probability. If the
spinner lands on a line it is spun again.
16.
P(pointer landing on blue)
SOLUTION:
The spinner is divided into 5 sectors.
The ratio of the
area of a sector of a circle to the area of the entire
circle is the same as the ratio of the sector
’
s central
angle to 360.The measure of the sector colored in
blue is 84
º
. Therefore, the probability that the pointer
will land on blue is
ANSWER:
23.3%
18.
P(pointer landing on red)
SOLUTION:
The spinner is divided into 5 sectors.
The ratio of the
area of a sector of a circle to the area of the entire
circle is the same as the ratio of the sector
’
s central
angle to 360.The measure of the sector colored in
red is 92
º
. Therefore, the probability that the pointer
will land on red is
ANSWER:
25.6%
Describe an event with a 33% probability for
each model.
20.
SOLUTION:
There are three possible outcomes red, yellow and
green lights and the probability of each outcome is
ANSWER:
Sample answer: getting a red light
22.
SOLUTION:
The spinner is divided into 6 equal sectors of two
colors
each. So, landing on any particular color has a
probability of
ANSWER:
Sample answer: landing on green
Find the probability that a point chosen at
random lies in the shaded region.
24.
SOLUTION:
The length of each side of the large triangle is 14
units. The triangle is equilateral, so we can split it into
two 30-60-90 triangles to find the height. The height
is .
The area of the large triangle is
.
The length of each side of the small triangles is 4
units. The triangles are equilateral, so we can split
them into two 30-60-90 triangles to find the height.
The height is .
The combined area of the small triangles is
.
The probability that a point
chosen at random lies in
the shaded region is .
ANSWER:
0.755 or 75.5%
26.
FARMING
The layout for a farm is shown with
each square representing a plot. Estimate the area of
each field to answer each question.
a.
What is the approximate combined area of the
spinach and corn fields?
b.
Find the probability that a randomly chosen plot is
used to grow soybeans.
SOLUTION:
a.
Count the number of squares to find the
approximate area of the
spinach and corn fields.
There are 64 complete squares and 5 half squares.
Therefore the approximate area is
b.
The total area of the farm is 10(17) = 170 sq.
units. and the area of the soybean field is about
Therefore,theprobabilityis
.
ANSWER:
a.
67 square units
b.
0.16 or 16%
28.
COORDINATE GEOMETRY
If a point is chosen
at random in the coordinate grid, find each
probability. Round to the nearest hundredth.
a.
P(point inside the circle)
b.
P(point inside the trapezoid)
c.
P(point inside the trapezoid, square, or circle)
SOLUTION:
The total area of the coordinate grid is 100 sq. units.
a.
The radius of the circle is 2 units. The area of the
circle is
Therefore, the probability that a point chosen is inside
the circle is
b.
The lengths of the bases of the trapezoid are 2 and
4unitsandtheheightis3units.
The area of the trapezoid is
Therefore, the probability that a point chosen is inside
the trapezoid is
c.
The length of each side of the square is .
Theareaofthesquareis8squareunits.
The sum of the area of the circle, trapezoid, and
square is 4
π
+ 8 + 9
≈
30 sq. units.
Therefore, the probability that a point chosen is inside
the
trapezoid, square, or circle
is about
ANSWER:
a.
, 0.13, or 13%
b.
, 0.09, or 9%
c.
, 0.30, or 30%
CCSS SENSE-
MAKING
Find the probability
that a point chosen at random lies in a shaded
region.
30.
SOLUTION:
There are three circles with radius 3 units in a row
and two in a column . The length of the rectangle is
18unitsandthewidthis6units.
The area of each circle is
π
(3)
2
= 9
π
units
2
.
The area of the rectangle is 12(18) = 216 units
2
.
Theareaoftheshadedregionis216–
6(9
π
) = 46.4
units
2
.
Therefore, the probability is about
ANSWER:
0.21 or 21%
CCSSREASONING
Point X is chosen at
random on
. Find the probability of each
event.
6.
P(X is on )
SOLUTION:
ANSWER:
, 0.44, or 44%
8.
P(X is on )
SOLUTION:
ANSWER:
, 0.56, or 56%
10.
BIRDS
Four birds are sitting on a telephone wire.
What is the probability that a fifth bird landing at a
randomly selected point on the wire will sit at some
point between birds 3 and 4?
SOLUTION:
ANSWER:
, 0.33, or 33%
Find the probability that a point chosen at
random lies in the shaded region.
12.
SOLUTION:
ANSWER:
, 0.375 or 37.5%
14.
SOLUTION:
If a region A contains a region B and a point E in
region A is chosen at random, then the probability
that point E is in region B is
The area of a regular polygon is the half the product
of the apothem and the perimeter. Find the apothem.
The length of the apothem of an hexagon of side
length a units is
Area of the large hexagon:
Area of the small hexagons:

The area of the shaded region is
.
Therefore, the probability is
ANSWER:
, 0.4375, or 43.75%
Use the spinner to find each probability. If the
spinner lands on a line it is spun again.
16.
P(pointer landing on blue)
SOLUTION:
The spinner is divided into 5 sectors.
The ratio of the
area of a sector of a circle to the area of the entire
circle is the same as the ratio of the sector
’
s central
angle to 360.The measure of the sector colored in
blue is 84
º
. Therefore, the probability that the pointer
will land on blue is
ANSWER:
23.3%
18.
P(pointer landing on red)
SOLUTION:
The spinner is divided into 5 sectors.
The ratio of the
area of a sector of a circle to the area of the entire
circle is the same as the ratio of the sector
’
s central
angle to 360.The measure of the sector colored in
red is 92
º
. Therefore, the probability that the pointer
will land on red is
ANSWER:
25.6%
Describe an event with a 33% probability for
each model.
20.
SOLUTION:
There are three possible outcomes red, yellow and
green lights and the probability of each outcome is
ANSWER:
Sample answer: getting a red light
22.
SOLUTION:
The spinner is divided into 6 equal sectors of two
colors
each. So, landing on any particular color has a
probability of
ANSWER:
Sample answer: landing on green
Find the probability that a point chosen at
random lies in the shaded region.
24.
SOLUTION:
The length of each side of the large triangle is 14
units. The triangle is equilateral, so we can split it into
two 30-60-90 triangles to find the height. The height
is .
The area of the large triangle is
.
The length of each side of the small triangles is 4
units. The triangles are equilateral, so we can split
them into two 30-60-90 triangles to find the height.
The height is .
The combined area of the small triangles is
.
The probability that a point
chosen at random lies in
the shaded region is .
ANSWER:
0.755 or 75.5%
26.
FARMING
The layout for a farm is shown with
each square representing a plot. Estimate the area of
each field to answer each question.
a.
What is the approximate combined area of the
spinach and corn fields?
b.
Find the probability that a randomly chosen plot is
used to grow soybeans.
SOLUTION:
a.
Count the number of squares to find the
approximate area of the
spinach and corn fields.
There are 64 complete squares and 5 half squares.
Therefore the approximate area is
b.
The total area of the farm is 10(17) = 170 sq.
units. and the area of the soybean field is about
Therefore,theprobabilityis
.
ANSWER:
a.
67 square units
b.
0.16 or 16%
28.
COORDINATE GEOMETRY
If a point is chosen
at random in the coordinate grid, find each
probability. Round to the nearest hundredth.
a.
P(point inside the circle)
b.
P(point inside the trapezoid)
c.
P(point inside the trapezoid, square, or circle)
SOLUTION:
The total area of the coordinate grid is 100 sq. units.
a.
The radius of the circle is 2 units. The area of the
circle is
Therefore, the probability that a point chosen is inside
the circle is
b.
The lengths of the bases of the trapezoid are 2 and
4unitsandtheheightis3units.
The area of the trapezoid is
Therefore, the probability that a point chosen is inside
the trapezoid is
c.
The length of each side of the square is .
Theareaofthesquareis8squareunits.
The sum of the area of the circle, trapezoid, and
square is 4
π
+ 8 + 9
≈
30 sq. units.
Therefore, the probability that a point chosen is inside
the
trapezoid, square, or circle
is about
ANSWER:
a.
, 0.13, or 13%
b.
, 0.09, or 9%
c.
, 0.30, or 30%
CCSS SENSE-
MAKING
Find the probability
that a point chosen at random lies in a shaded
region.
30.
SOLUTION:
There are three circles with radius 3 units in a row
and two in a column . The length of the rectangle is
18unitsandthewidthis6units.
The area of each circle is
π
(3)
2
= 9
π
units
2
.
The area of the rectangle is 12(18) = 216 units
2
.
Theareaoftheshadedregionis216–
6(9
π
) = 46.4
units
2
.
Therefore, the probability is about
ANSWER:
0.21 or 21%
eSolutionsManual-PoweredbyCogneroPage1
13-3 Geometric Probability
CCSSREASONING
Point X is chosen at
random on
. Find the probability of each
event.
6.
P(X is on )
SOLUTION:
ANSWER:
, 0.44, or 44%
8.
P(X is on )
SOLUTION:
ANSWER:
, 0.56, or 56%
10.
BIRDS
Four birds are sitting on a telephone wire.
What is the probability that a fifth bird landing at a
randomly selected point on the wire will sit at some
point between birds 3 and 4?
SOLUTION:
ANSWER:
, 0.33, or 33%
Find the probability that a point chosen at
random lies in the shaded region.
12.
SOLUTION:
ANSWER:
, 0.375 or 37.5%
14.
SOLUTION:
If a region A contains a region B and a point E in
region A is chosen at random, then the probability
that point E is in region B is
The area of a regular polygon is the half the product
of the apothem and the perimeter. Find the apothem.
The length of the apothem of an hexagon of side
length a units is
Area of the large hexagon:
Area of the small hexagons:

The area of the shaded region is
.
Therefore, the probability is
ANSWER:
, 0.4375, or 43.75%
Use the spinner to find each probability. If the
spinner lands on a line it is spun again.
16.
P(pointer landing on blue)
SOLUTION:
The spinner is divided into 5 sectors.
The ratio of the
area of a sector of a circle to the area of the entire
circle is the same as the ratio of the sector
’
s central
angle to 360.The measure of the sector colored in
blue is 84
º
. Therefore, the probability that the pointer
will land on blue is
ANSWER:
23.3%
18.
P(pointer landing on red)
SOLUTION:
The spinner is divided into 5 sectors.
The ratio of the
area of a sector of a circle to the area of the entire
circle is the same as the ratio of the sector
’
s central
angle to 360.The measure of the sector colored in
red is 92
º
. Therefore, the probability that the pointer
will land on red is
ANSWER:
25.6%
Describe an event with a 33% probability for
each model.
20.
SOLUTION:
There are three possible outcomes red, yellow and
green lights and the probability of each outcome is
ANSWER:
Sample answer: getting a red light
22.
SOLUTION:
The spinner is divided into 6 equal sectors of two
colors
each. So, landing on any particular color has a
probability of
ANSWER:
Sample answer: landing on green
Find the probability that a point chosen at
random lies in the shaded region.
24.
SOLUTION:
The length of each side of the large triangle is 14
units. The triangle is equilateral, so we can split it into
two 30-60-90 triangles to find the height. The height
is .
The area of the large triangle is
.
The length of each side of the small triangles is 4
units. The triangles are equilateral, so we can split
them into two 30-60-90 triangles to find the height.
The height is .
The combined area of the small triangles is
.
The probability that a point
chosen at random lies in
the shaded region is .
ANSWER:
0.755 or 75.5%
26.
FARMING
The layout for a farm is shown with
each square representing a plot. Estimate the area of
each field to answer each question.
a.
What is the approximate combined area of the
spinach and corn fields?
b.
Find the probability that a randomly chosen plot is
used to grow soybeans.
SOLUTION:
a.
Count the number of squares to find the
approximate area of the
spinach and corn fields.
There are 64 complete squares and 5 half squares.
Therefore the approximate area is
b.
The total area of the farm is 10(17) = 170 sq.
units. and the area of the soybean field is about
Therefore,theprobabilityis
.
ANSWER:
a.
67 square units
b.
0.16 or 16%
28.
COORDINATE GEOMETRY
If a point is chosen
at random in the coordinate grid, find each
probability. Round to the nearest hundredth.
a.
P(point inside the circle)
b.
P(point inside the trapezoid)
c.
P(point inside the trapezoid, square, or circle)
SOLUTION:
The total area of the coordinate grid is 100 sq. units.
a.
The radius of the circle is 2 units. The area of the
circle is
Therefore, the probability that a point chosen is inside
the circle is
b.
The lengths of the bases of the trapezoid are 2 and
4unitsandtheheightis3units.
The area of the trapezoid is
Therefore, the probability that a point chosen is inside
the trapezoid is
c.
The length of each side of the square is .
Theareaofthesquareis8squareunits.
The sum of the area of the circle, trapezoid, and
square is 4
π
+ 8 + 9
≈
30 sq. units.
Therefore, the probability that a point chosen is inside
the
trapezoid, square, or circle
is about
ANSWER:
a.
, 0.13, or 13%
b.
, 0.09, or 9%
c.
, 0.30, or 30%
CCSS SENSE-
MAKING
Find the probability
that a point chosen at random lies in a shaded
region.
30.
SOLUTION:
There are three circles with radius 3 units in a row
and two in a column . The length of the rectangle is
18unitsandthewidthis6units.
The area of each circle is
π
(3)
2
= 9
π
units
2
.
The area of the rectangle is 12(18) = 216 units
2
.
Theareaoftheshadedregionis216–
6(9
π
) = 46.4
units
2
.
Therefore, the probability is about
ANSWER:
0.21 or 21%
CCSSREASONING
Point X is chosen at
random on
. Find the probability of each
event.
6.
P(X is on )
SOLUTION:
ANSWER:
, 0.44, or 44%
8.
P(X is on )
SOLUTION:
ANSWER:
, 0.56, or 56%
10.
BIRDS
Four birds are sitting on a telephone wire.
What is the probability that a fifth bird landing at a
randomly selected point on the wire will sit at some
point between birds 3 and 4?
SOLUTION:
ANSWER:
, 0.33, or 33%
Find the probability that a point chosen at
random lies in the shaded region.
12.
SOLUTION:
ANSWER:
, 0.375 or 37.5%
14.
SOLUTION:
If a region A contains a region B and a point E in
region A is chosen at random, then the probability
that point E is in region B is
The area of a regular polygon is the half the product
of the apothem and the perimeter. Find the apothem.
The length of the apothem of an hexagon of side
length a units is
Area of the large hexagon:
Area of the small hexagons:

The area of the shaded region is
.
Therefore, the probability is
ANSWER:
, 0.4375, or 43.75%
Use the spinner to find each probability. If the
spinner lands on a line it is spun again.
16.
P(pointer landing on blue)
SOLUTION:
The spinner is divided into 5 sectors.
The ratio of the
area of a sector of a circle to the area of the entire
circle is the same as the ratio of the sector
’
s central
angle to 360.The measure of the sector colored in
blue is 84
º
. Therefore, the probability that the pointer
will land on blue is
ANSWER:
23.3%
18.
P(pointer landing on red)
SOLUTION:
The spinner is divided into 5 sectors.
The ratio of the
area of a sector of a circle to the area of the entire
circle is the same as the ratio of the sector
’
s central
angle to 360.The measure of the sector colored in
red is 92
º
. Therefore, the probability that the pointer
will land on red is
ANSWER:
25.6%
Describe an event with a 33% probability for
each model.
20.
SOLUTION:
There are three possible outcomes red, yellow and
green lights and the probability of each outcome is
ANSWER:
Sample answer: getting a red light
22.
SOLUTION:
The spinner is divided into 6 equal sectors of two
colors
each. So, landing on any particular color has a
probability of
ANSWER:
Sample answer: landing on green
Find the probability that a point chosen at
random lies in the shaded region.
24.
SOLUTION:
The length of each side of the large triangle is 14
units. The triangle is equilateral, so we can split it into
two 30-60-90 triangles to find the height. The height
is .
The area of the large triangle is
.
The length of each side of the small triangles is 4
units. The triangles are equilateral, so we can split
them into two 30-60-90 triangles to find the height.
The height is .
The combined area of the small triangles is
.
The probability that a point
chosen at random lies in
the shaded region is .
ANSWER:
0.755 or 75.5%
26.
FARMING
The layout for a farm is shown with
each square representing a plot. Estimate the area of
each field to answer each question.
a.
What is the approximate combined area of the
spinach and corn fields?
b.
Find the probability that a randomly chosen plot is
used to grow soybeans.
SOLUTION:
a.
Count the number of squares to find the
approximate area of the
spinach and corn fields.
There are 64 complete squares and 5 half squares.
Therefore the approximate area is
b.
The total area of the farm is 10(17) = 170 sq.
units. and the area of the soybean field is about
Therefore,theprobabilityis
.
ANSWER:
a.
67 square units
b.
0.16 or 16%
28.
COORDINATE GEOMETRY
If a point is chosen
at random in the coordinate grid, find each
probability. Round to the nearest hundredth.
a.
P(point inside the circle)
b.
P(point inside the trapezoid)
c.
P(point inside the trapezoid, square, or circle)
SOLUTION:
The total area of the coordinate grid is 100 sq. units.
a.
The radius of the circle is 2 units. The area of the
circle is
Therefore, the probability that a point chosen is inside
the circle is
b.
The lengths of the bases of the trapezoid are 2 and
4unitsandtheheightis3units.
The area of the trapezoid is
Therefore, the probability that a point chosen is inside
the trapezoid is
c.
The length of each side of the square is .
Theareaofthesquareis8squareunits.
The sum of the area of the circle, trapezoid, and
square is 4
π
+ 8 + 9
≈
30 sq. units.
Therefore, the probability that a point chosen is inside
the
trapezoid, square, or circle
is about
ANSWER:
a.
, 0.13, or 13%
b.
, 0.09, or 9%
c.
, 0.30, or 30%
CCSS SENSE-
MAKING
Find the probability
that a point chosen at random lies in a shaded
region.
30.
SOLUTION:
There are three circles with radius 3 units in a row
and two in a column . The length of the rectangle is
18unitsandthewidthis6units.
The area of each circle is
π
(3)
2
= 9
π
units
2
.
The area of the rectangle is 12(18) = 216 units
2
.
Theareaoftheshadedregionis216–
6(9
π
) = 46.4
units
2
.
Therefore, the probability is about
ANSWER:
0.21 or 21%
eSolutionsManual-PoweredbyCogneroPage2
13-3 Geometric Probability
CCSSREASONING
Point X is chosen at
random on
. Find the probability of each
event.
6.
P(X is on )
SOLUTION:
ANSWER:
, 0.44, or 44%
8.
P(X is on )
SOLUTION:
ANSWER:
, 0.56, or 56%
10.
BIRDS
Four birds are sitting on a telephone wire.
What is the probability that a fifth bird landing at a
randomly selected point on the wire will sit at some
point between birds 3 and 4?
SOLUTION:
ANSWER:
, 0.33, or 33%
Find the probability that a point chosen at
random lies in the shaded region.
12.
SOLUTION:
ANSWER:
, 0.375 or 37.5%
14.
SOLUTION:
If a region A contains a region B and a point E in
region A is chosen at random, then the probability
that point E is in region B is
The area of a regular polygon is the half the product
of the apothem and the perimeter. Find the apothem.
The length of the apothem of an hexagon of side
length a units is
Area of the large hexagon:
Area of the small hexagons:

The area of the shaded region is
.
Therefore, the probability is
ANSWER:
, 0.4375, or 43.75%
Use the spinner to find each probability. If the
spinner lands on a line it is spun again.
16.
P(pointer landing on blue)
SOLUTION:
The spinner is divided into 5 sectors.
The ratio of the
area of a sector of a circle to the area of the entire
circle is the same as the ratio of the sector
’
s central
angle to 360.The measure of the sector colored in
blue is 84
º
. Therefore, the probability that the pointer
will land on blue is
ANSWER:
23.3%
18.
P(pointer landing on red)
SOLUTION:
The spinner is divided into 5 sectors.
The ratio of the
area of a sector of a circle to the area of the entire
circle is the same as the ratio of the sector
’
s central
angle to 360.The measure of the sector colored in
red is 92
º
. Therefore, the probability that the pointer
will land on red is
ANSWER:
25.6%
Describe an event with a 33% probability for
each model.
20.
SOLUTION:
There are three possible outcomes red, yellow and
green lights and the probability of each outcome is
ANSWER:
Sample answer: getting a red light
22.
SOLUTION:
The spinner is divided into 6 equal sectors of two
colors
each. So, landing on any particular color has a
probability of
ANSWER:
Sample answer: landing on green
Find the probability that a point chosen at
random lies in the shaded region.
24.
SOLUTION:
The length of each side of the large triangle is 14
units. The triangle is equilateral, so we can split it into
two 30-60-90 triangles to find the height. The height
is .
The area of the large triangle is
.
The length of each side of the small triangles is 4
units. The triangles are equilateral, so we can split
them into two 30-60-90 triangles to find the height.
The height is .
The combined area of the small triangles is
.
The probability that a point
chosen at random lies in
the shaded region is .
ANSWER:
0.755 or 75.5%
26.
FARMING
The layout for a farm is shown with
each square representing a plot. Estimate the area of
each field to answer each question.
a.
What is the approximate combined area of the
spinach and corn fields?
b.
Find the probability that a randomly chosen plot is
used to grow soybeans.
SOLUTION:
a.
Count the number of squares to find the
approximate area of the
spinach and corn fields.
There are 64 complete squares and 5 half squares.
Therefore the approximate area is
b.
The total area of the farm is 10(17) = 170 sq.
units. and the area of the soybean field is about
Therefore,theprobabilityis
.
ANSWER:
a.
67 square units
b.
0.16 or 16%
28.
COORDINATE GEOMETRY
If a point is chosen
at random in the coordinate grid, find each
probability. Round to the nearest hundredth.
a.
P(point inside the circle)
b.
P(point inside the trapezoid)
c.
P(point inside the trapezoid, square, or circle)
SOLUTION:
The total area of the coordinate grid is 100 sq. units.
a.
The radius of the circle is 2 units. The area of the
circle is
Therefore, the probability that a point chosen is inside
the circle is
b.
The lengths of the bases of the trapezoid are 2 and
4unitsandtheheightis3units.
The area of the trapezoid is
Therefore, the probability that a point chosen is inside
the trapezoid is
c.
The length of each side of the square is .
Theareaofthesquareis8squareunits.
The sum of the area of the circle, trapezoid, and
square is 4
π
+ 8 + 9
≈
30 sq. units.
Therefore, the probability that a point chosen is inside
the
trapezoid, square, or circle
is about
ANSWER:
a.
, 0.13, or 13%
b.
, 0.09, or 9%
c.
, 0.30, or 30%
CCSS SENSE-
MAKING
Find the probability
that a point chosen at random lies in a shaded
region.
30.
SOLUTION:
There are three circles with radius 3 units in a row
and two in a column . The length of the rectangle is
18unitsandthewidthis6units.
The area of each circle is
π
(3)
2
= 9
π
units
2
.
The area of the rectangle is 12(18) = 216 units
2
.
Theareaoftheshadedregionis216–
6(9
π
) = 46.4
units
2
.
Therefore, the probability is about
ANSWER:
0.21 or 21%
CCSSREASONING
Point X is chosen at
random on
. Find the probability of each
event.
6.
P(X is on )
SOLUTION:
ANSWER:
, 0.44, or 44%
8.
P(X is on )
SOLUTION:
ANSWER:
, 0.56, or 56%
10.
BIRDS
Four birds are sitting on a telephone wire.
What is the probability that a fifth bird landing at a
randomly selected point on the wire will sit at some
point between birds 3 and 4?
SOLUTION:
ANSWER:
, 0.33, or 33%
Find the probability that a point chosen at
random lies in the shaded region.
12.
SOLUTION:
ANSWER:
, 0.375 or 37.5%
14.
SOLUTION:
If a region A contains a region B and a point E in
region A is chosen at random, then the probability
that point E is in region B is
The area of a regular polygon is the half the product
of the apothem and the perimeter. Find the apothem.
The length of the apothem of an hexagon of side
length a units is
Area of the large hexagon:
Area of the small hexagons:

The area of the shaded region is
.
Therefore, the probability is
ANSWER:
, 0.4375, or 43.75%
Use the spinner to find each probability. If the
spinner lands on a line it is spun again.
16.
P(pointer landing on blue)
SOLUTION:
The spinner is divided into 5 sectors.
The ratio of the
area of a sector of a circle to the area of the entire
circle is the same as the ratio of the sector
’
s central
angle to 360.The measure of the sector colored in
blue is 84
º
. Therefore, the probability that the pointer
will land on blue is
ANSWER:
23.3%
18.
P(pointer landing on red)
SOLUTION:
The spinner is divided into 5 sectors.
The ratio of the
area of a sector of a circle to the area of the entire
circle is the same as the ratio of the sector
’
s central
angle to 360.The measure of the sector colored in
red is 92
º
. Therefore, the probability that the pointer
will land on red is
ANSWER:
25.6%
Describe an event with a 33% probability for
each model.
20.
SOLUTION:
There are three possible outcomes red, yellow and
green lights and the probability of each outcome is
ANSWER:
Sample answer: getting a red light
22.
SOLUTION:
The spinner is divided into 6 equal sectors of two
colors
each. So, landing on any particular color has a
probability of
ANSWER:
Sample answer: landing on green
Find the probability that a point chosen at
random lies in the shaded region.
24.
SOLUTION:
The length of each side of the large triangle is 14
units. The triangle is equilateral, so we can split it into
two 30-60-90 triangles to find the height. The height
is .
The area of the large triangle is
.
The length of each side of the small triangles is 4
units. The triangles are equilateral, so we can split
them into two 30-60-90 triangles to find the height.
The height is .
The combined area of the small triangles is
.
The probability that a point
chosen at random lies in
the shaded region is .
ANSWER:
0.755 or 75.5%
26.
FARMING
The layout for a farm is shown with
each square representing a plot. Estimate the area of
each field to answer each question.
a.
What is the approximate combined area of the
spinach and corn fields?
b.
Find the probability that a randomly chosen plot is
used to grow soybeans.
SOLUTION:
a.
Count the number of squares to find the
approximate area of the
spinach and corn fields.
There are 64 complete squares and 5 half squares.
Therefore the approximate area is
b.
The total area of the farm is 10(17) = 170 sq.
units. and the area of the soybean field is about
Therefore,theprobabilityis
.
ANSWER:
a.
67 square units
b.
0.16 or 16%
28.
COORDINATE GEOMETRY
If a point is chosen
at random in the coordinate grid, find each
probability. Round to the nearest hundredth.
a.
P(point inside the circle)
b.
P(point inside the trapezoid)
c.
P(point inside the trapezoid, square, or circle)
SOLUTION:
The total area of the coordinate grid is 100 sq. units.
a.
The radius of the circle is 2 units. The area of the
circle is
Therefore, the probability that a point chosen is inside
the circle is
b.
The lengths of the bases of the trapezoid are 2 and
4unitsandtheheightis3units.
The area of the trapezoid is
Therefore, the probability that a point chosen is inside
the trapezoid is
c.
The length of each side of the square is .
Theareaofthesquareis8squareunits.
The sum of the area of the circle, trapezoid, and
square is 4
π
+ 8 + 9
≈
30 sq. units.
Therefore, the probability that a point chosen is inside
the
trapezoid, square, or circle
is about
ANSWER:
a.
, 0.13, or 13%
b.
, 0.09, or 9%
c.
, 0.30, or 30%
CCSS SENSE-
MAKING
Find the probability
that a point chosen at random lies in a shaded
region.
30.
SOLUTION:
There are three circles with radius 3 units in a row
and two in a column . The length of the rectangle is
18unitsandthewidthis6units.
The area of each circle is
π
(3)
2
= 9
π
units
2
.
The area of the rectangle is 12(18) = 216 units
2
.
Theareaoftheshadedregionis216–
6(9
π
) = 46.4
units
2
.
Therefore, the probability is about
ANSWER:
0.21 or 21%
eSolutionsManual-PoweredbyCogneroPage3
13-3 Geometric Probability
CCSSREASONING
Point X is chosen at
random on
. Find the probability of each
event.
6.
P(X is on )
SOLUTION:
ANSWER:
, 0.44, or 44%
8.
P(X is on )
SOLUTION:
ANSWER:
, 0.56, or 56%
10.
BIRDS
Four birds are sitting on a telephone wire.
What is the probability that a fifth bird landing at a
randomly selected point on the wire will sit at some
point between birds 3 and 4?
SOLUTION:
ANSWER:
, 0.33, or 33%
Find the probability that a point chosen at
random lies in the shaded region.
12.
SOLUTION:
ANSWER:
, 0.375 or 37.5%
14.
SOLUTION:
If a region A contains a region B and a point E in
region A is chosen at random, then the probability
that point E is in region B is
The area of a regular polygon is the half the product
of the apothem and the perimeter. Find the apothem.
The length of the apothem of an hexagon of side
length a units is
Area of the large hexagon:
Area of the small hexagons:

The area of the shaded region is
.
Therefore, the probability is
ANSWER:
, 0.4375, or 43.75%
Use the spinner to find each probability. If the
spinner lands on a line it is spun again.
16.
P(pointer landing on blue)
SOLUTION:
The spinner is divided into 5 sectors.
The ratio of the
area of a sector of a circle to the area of the entire
circle is the same as the ratio of the sector
’
s central
angle to 360.The measure of the sector colored in
blue is 84
º
. Therefore, the probability that the pointer
will land on blue is
ANSWER:
23.3%
18.
P(pointer landing on red)
SOLUTION:
The spinner is divided into 5 sectors.
The ratio of the
area of a sector of a circle to the area of the entire
circle is the same as the ratio of the sector
’
s central
angle to 360.The measure of the sector colored in
red is 92
º
. Therefore, the probability that the pointer
will land on red is
ANSWER:
25.6%
Describe an event with a 33% probability for
each model.
20.
SOLUTION:
There are three possible outcomes red, yellow and
green lights and the probability of each outcome is
ANSWER:
Sample answer: getting a red light
22.
SOLUTION:
The spinner is divided into 6 equal sectors of two
colors
each. So, landing on any particular color has a
probability of
ANSWER:
Sample answer: landing on green
Find the probability that a point chosen at
random lies in the shaded region.
24.
SOLUTION:
The length of each side of the large triangle is 14
units. The triangle is equilateral, so we can split it into
two 30-60-90 triangles to find the height. The height
is .
The area of the large triangle is
.
The length of each side of the small triangles is 4
units. The triangles are equilateral, so we can split
them into two 30-60-90 triangles to find the height.
The height is .
The combined area of the small triangles is
.
The probability that a point
chosen at random lies in
the shaded region is .
ANSWER:
0.755 or 75.5%
26.
FARMING
The layout for a farm is shown with
each square representing a plot. Estimate the area of
each field to answer each question.
a.
What is the approximate combined area of the
spinach and corn fields?
b.
Find the probability that a randomly chosen plot is
used to grow soybeans.
SOLUTION:
a.
Count the number of squares to find the
approximate area of the
spinach and corn fields.
There are 64 complete squares and 5 half squares.
Therefore the approximate area is
b.
The total area of the farm is 10(17) = 170 sq.
units. and the area of the soybean field is about
Therefore,theprobabilityis
.
ANSWER:
a.
67 square units
b.
0.16 or 16%
28.
COORDINATE GEOMETRY
If a point is chosen
at random in the coordinate grid, find each
probability. Round to the nearest hundredth.
a.
P(point inside the circle)
b.
P(point inside the trapezoid)
c.
P(point inside the trapezoid, square, or circle)
SOLUTION:
The total area of the coordinate grid is 100 sq. units.
a.
The radius of the circle is 2 units. The area of the
circle is
Therefore, the probability that a point chosen is inside
the circle is
b.
The lengths of the bases of the trapezoid are 2 and
4unitsandtheheightis3units.
The area of the trapezoid is
Therefore, the probability that a point chosen is inside
the trapezoid is
c.
The length of each side of the square is .
Theareaofthesquareis8squareunits.
The sum of the area of the circle, trapezoid, and
square is 4
π
+ 8 + 9
≈
30 sq. units.
Therefore, the probability that a point chosen is inside
the
trapezoid, square, or circle
is about
ANSWER:
a.
, 0.13, or 13%
b.
, 0.09, or 9%
c.
, 0.30, or 30%
CCSS SENSE-
MAKING
Find the probability
that a point chosen at random lies in a shaded
region.
30.
SOLUTION:
There are three circles with radius 3 units in a row
and two in a column . The length of the rectangle is
18unitsandthewidthis6units.
The area of each circle is
π
(3)
2
= 9
π
units
2
.
The area of the rectangle is 12(18) = 216 units
2
.
Theareaoftheshadedregionis216–
6(9
π
) = 46.4
units
2
.
Therefore, the probability is about
ANSWER:
0.21 or 21%
CCSSREASONING
Point X is chosen at
random on
. Find the probability of each
event.
6.
P(X is on )
SOLUTION:
ANSWER:
, 0.44, or 44%
8.
P(X is on )
SOLUTION:
ANSWER:
, 0.56, or 56%
10.
BIRDS
Four birds are sitting on a telephone wire.
What is the probability that a fifth bird landing at a
randomly selected point on the wire will sit at some
point between birds 3 and 4?
SOLUTION:
ANSWER:
, 0.33, or 33%
Find the probability that a point chosen at
random lies in the shaded region.
12.
SOLUTION:
ANSWER:
, 0.375 or 37.5%
14.
SOLUTION:
If a region A contains a region B and a point E in
region A is chosen at random, then the probability
that point E is in region B is
The area of a regular polygon is the half the product
of the apothem and the perimeter. Find the apothem.
The length of the apothem of an hexagon of side
length a units is
Area of the large hexagon:
Area of the small hexagons:

The area of the shaded region is
.
Therefore, the probability is
ANSWER:
, 0.4375, or 43.75%
Use the spinner to find each probability. If the
spinner lands on a line it is spun again.
16.
P(pointer landing on blue)
SOLUTION:
The spinner is divided into 5 sectors.
The ratio of the
area of a sector of a circle to the area of the entire
circle is the same as the ratio of the sector
’
s central
angle to 360.The measure of the sector colored in
blue is 84
º
. Therefore, the probability that the pointer
will land on blue is
ANSWER:
23.3%
18.
P(pointer landing on red)
SOLUTION:
The spinner is divided into 5 sectors.
The ratio of the
area of a sector of a circle to the area of the entire
circle is the same as the ratio of the sector
’
s central
angle to 360.The measure of the sector colored in
red is 92
º
. Therefore, the probability that the pointer
will land on red is
ANSWER:
25.6%
Describe an event with a 33% probability for
each model.
20.
SOLUTION:
There are three possible outcomes red, yellow and
green lights and the probability of each outcome is
ANSWER:
Sample answer: getting a red light
22.
SOLUTION:
The spinner is divided into 6 equal sectors of two
colors
each. So, landing on any particular color has a
probability of
ANSWER:
Sample answer: landing on green
Find the probability that a point chosen at
random lies in the shaded region.
24.
SOLUTION:
The length of each side of the large triangle is 14
units. The triangle is equilateral, so we can split it into
two 30-60-90 triangles to find the height. The height
is .
The area of the large triangle is
.
The length of each side of the small triangles is 4
units. The triangles are equilateral, so we can split
them into two 30-60-90 triangles to find the height.
The height is .
The combined area of the small triangles is
.
The probability that a point
chosen at random lies in
the shaded region is .
ANSWER:
0.755 or 75.5%
26.
FARMING
The layout for a farm is shown with
each square representing a plot. Estimate the area of
each field to answer each question.
a.
What is the approximate combined area of the
spinach and corn fields?
b.
Find the probability that a randomly chosen plot is
used to grow soybeans.
SOLUTION:
a.
Count the number of squares to find the
approximate area of the
spinach and corn fields.
There are 64 complete squares and 5 half squares.
Therefore the approximate area is
b.
The total area of the farm is 10(17) = 170 sq.
units. and the area of the soybean field is about
Therefore,theprobabilityis
.
ANSWER:
a.
67 square units
b.
0.16 or 16%
28.
COORDINATE GEOMETRY
If a point is chosen
at random in the coordinate grid, find each
probability. Round to the nearest hundredth.
a.
P(point inside the circle)
b.
P(point inside the trapezoid)
c.
P(point inside the trapezoid, square, or circle)
SOLUTION:
The total area of the coordinate grid is 100 sq. units.
a.
The radius of the circle is 2 units. The area of the
circle is
Therefore, the probability that a point chosen is inside
the circle is
b.
The lengths of the bases of the trapezoid are 2 and
4unitsandtheheightis3units.
The area of the trapezoid is
Therefore, the probability that a point chosen is inside
the trapezoid is
c.
The length of each side of the square is .
Theareaofthesquareis8squareunits.
The sum of the area of the circle, trapezoid, and
square is 4
π
+ 8 + 9
≈
30 sq. units.
Therefore, the probability that a point chosen is inside
the
trapezoid, square, or circle
is about
ANSWER:
a.
, 0.13, or 13%
b.
, 0.09, or 9%
c.
, 0.30, or 30%
CCSS SENSE-
MAKING
Find the probability
that a point chosen at random lies in a shaded
region.
30.
SOLUTION:
There are three circles with radius 3 units in a row
and two in a column . The length of the rectangle is
18unitsandthewidthis6units.
The area of each circle is
π
(3)
2
= 9
π
units
2
.
The area of the rectangle is 12(18) = 216 units
2
.
Theareaoftheshadedregionis216–
6(9
π
) = 46.4
units
2
.
Therefore, the probability is about
ANSWER:
0.21 or 21%
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13-3 Geometric Probability
CCSSREASONING
Point X is chosen at
random on
. Find the probability of each
event.
6.
P(X is on )
SOLUTION:
ANSWER:
, 0.44, or 44%
8.
P(X is on )
SOLUTION:
ANSWER:
, 0.56, or 56%
10.
BIRDS
Four birds are sitting on a telephone wire.
What is the probability that a fifth bird landing at a
randomly selected point on the wire will sit at some
point between birds 3 and 4?
SOLUTION:
ANSWER:
, 0.33, or 33%
Find the probability that a point chosen at
random lies in the shaded region.
12.
SOLUTION:
ANSWER:
, 0.375 or 37.5%
14.
SOLUTION:
If a region A contains a region B and a point E in
region A is chosen at random, then the probability
that point E is in region B is
The area of a regular polygon is the half the product
of the apothem and the perimeter. Find the apothem.
The length of the apothem of an hexagon of side
length a units is
Area of the large hexagon:
Area of the small hexagons:

The area of the shaded region is
.
Therefore, the probability is
ANSWER:
, 0.4375, or 43.75%
Use the spinner to find each probability. If the
spinner lands on a line it is spun again.
16.
P(pointer landing on blue)
SOLUTION:
The spinner is divided into 5 sectors.
The ratio of the
area of a sector of a circle to the area of the entire
circle is the same as the ratio of the sector
’
s central
angle to 360.The measure of the sector colored in
blue is 84
º
. Therefore, the probability that the pointer
will land on blue is
ANSWER:
23.3%
18.
P(pointer landing on red)
SOLUTION:
The spinner is divided into 5 sectors.
The ratio of the
area of a sector of a circle to the area of the entire
circle is the same as the ratio of the sector
’
s central
angle to 360.The measure of the sector colored in
red is 92
º
. Therefore, the probability that the pointer
will land on red is
ANSWER:
25.6%
Describe an event with a 33% probability for
each model.
20.
SOLUTION:
There are three possible outcomes red, yellow and
green lights and the probability of each outcome is
ANSWER:
Sample answer: getting a red light
22.
SOLUTION:
The spinner is divided into 6 equal sectors of two
colors
each. So, landing on any particular color has a
probability of
ANSWER:
Sample answer: landing on green
Find the probability that a point chosen at
random lies in the shaded region.
24.
SOLUTION:
The length of each side of the large triangle is 14
units. The triangle is equilateral, so we can split it into
two 30-60-90 triangles to find the height. The height
is .
The area of the large triangle is
.
The length of each side of the small triangles is 4
units. The triangles are equilateral, so we can split
them into two 30-60-90 triangles to find the height.
The height is .
The combined area of the small triangles is
.
The probability that a point
chosen at random lies in
the shaded region is .
ANSWER:
0.755 or 75.5%
26.
FARMING
The layout for a farm is shown with
each square representing a plot. Estimate the area of
each field to answer each question.
a.
What is the approximate combined area of the
spinach and corn fields?
b.
Find the probability that a randomly chosen plot is
used to grow soybeans.
SOLUTION:
a.
Count the number of squares to find the
approximate area of the
spinach and corn fields.
There are 64 complete squares and 5 half squares.
Therefore the approximate area is
b.
The total area of the farm is 10(17) = 170 sq.
units. and the area of the soybean field is about
Therefore,theprobabilityis
.
ANSWER:
a.
67 square units
b.
0.16 or 16%
28.
COORDINATE GEOMETRY
If a point is chosen
at random in the coordinate grid, find each
probability. Round to the nearest hundredth.
a.
P(point inside the circle)
b.
P(point inside the trapezoid)
c.
P(point inside the trapezoid, square, or circle)
SOLUTION:
The total area of the coordinate grid is 100 sq. units.
a.
The radius of the circle is 2 units. The area of the
circle is
Therefore, the probability that a point chosen is inside
the circle is
b.
The lengths of the bases of the trapezoid are 2 and
4unitsandtheheightis3units.
The area of the trapezoid is
Therefore, the probability that a point chosen is inside
the trapezoid is
c.
The length of each side of the square is .
Theareaofthesquareis8squareunits.
The sum of the area of the circle, trapezoid, and
square is 4
π
+ 8 + 9
≈
30 sq. units.
Therefore, the probability that a point chosen is inside
the
trapezoid, square, or circle
is about
ANSWER:
a.
, 0.13, or 13%
b.
, 0.09, or 9%
c.
, 0.30, or 30%
CCSS SENSE-
MAKING
Find the probability
that a point chosen at random lies in a shaded
region.
30.
SOLUTION:
There are three circles with radius 3 units in a row
and two in a column . The length of the rectangle is
18unitsandthewidthis6units.
The area of each circle is
π
(3)
2
= 9
π
units
2
.
The area of the rectangle is 12(18) = 216 units
2
.
Theareaoftheshadedregionis216–
6(9
π
) = 46.4
units
2
.
Therefore, the probability is about
ANSWER:
0.21 or 21%
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13-3 Geometric Probability