Name
LESSON
9-6
Date
Class
Practice B
Geometric Probability
_
A point is randomly chosen on AD . Find the
fractional probability of each event.
_
1. The point is on AB .
_
3. The point is on AD .
5
!
4
"
5
___
3
#
$
7
___
_
12
12
2
__
3
2. The point is on BD .
_
1
4. The point is not on BC .
Use the spinner to find the fractional probability of each event.
1
__
$
3
1
__
9
59
___
72
35
___
72
5. the pointer landing in region C
6. the pointer landing in region A
7. the pointer not landing in region D
8. the pointer landing in regions A or B
# 120°
0.21
0.20
0.41
0.59
10. the trapezoid
11. the circle or the trapezoid
12. not the circle and the trapezoid
135°
"
10 ft
Find the probability that a point chosen randomly
inside the rectangle is in each given shape. Round
answers to the nearest hundredth.
9. the circle
!
65°
40°
4 ft
4 ft
6 ft
2 ft
2 ft
Barb is practicing her chip shots on the chipping green at the
local golf club. Suppose Barb’s ball drops randomly on the chipping
green. The figure shows the chipping green in a grid whose squares
have 1-yard sides. There are 18 different 4.5-inch diameter holes
on the chipping green.
Possible answers based on an 11.5 yd2 estimate for the green:
13. Estimate the probability that Barb will chip her ball into any hole.
Round to the nearest thousandth.
0.019
14. Estimate the probability that Barb will chip her ball into the one
hole she is aiming for. Round to the nearest thousandth.
0.001
15. Estimate how many chip shots Barb will have to take to
ensure that one goes into a randomly selected hole.
16. Barb is getting frustrated, so her shots are even worse. Now
the ball drops randomly anywhere in the grid shown in the figure.
Estimate the probability that Barb will miss the chipping green. Round
to the nearest thousandth.
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
44
937 shots
0.425
Holt Geometry
Name
LESSON
9-6
Date
Class
Name
Practice A
LESSON
9-6
Geometric Probability
_
A point is randomly chosen on PS. Fill in the blanks and find the
probability of each event for Exercises 1–4.
8
4
2
QR
1. The point is on QR . P � _____ � ___ � ___
PS
18 9
2.
3
4. The point is not on BC .
18
3
walk
clear the
intersection
don�t walk
10
10
20
6. the pointer landing in region A
7. the pointer not landing in region D
8. the pointer landing in regions A or B
_1_
The total number of degrees in a circle is 360°. Use the
spinner to find the fractional probability of each event.
8. the pointer landing in regions B or C
9. the pointer landing in region A
10. the pointer not landing in region A
11. the circle or the trapezoid
0.17
12. the square
0.11
13. the triangle or the square
0.29
14. not the triangle
0.83
43
12. not the circle and the trapezoid
�
� 60° 90° 30°
�
�
����
����
����
2 ft
2 ft
Class
0.019
14. Estimate the probability that Barb will chip her ball into the one
hole she is aiming for. Round to the nearest thousandth.
0.001
����
937 shots
16. Barb is getting frustrated, so her shots are even worse. Now
the ball drops randomly anywhere in the grid shown in the figure.
Estimate the probability that Barb will miss the chipping green. Round
to the nearest thousandth.
Holt Geometry
44
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
Name
LESSON
9-6
Geometric Probability
Lightning strikes occur at random over the area of an electrical storm. A rate of
12 lightning strikes per minute is classified as excessive. One particular electrical
storm with excessive lightning covers a rectangular area of 25 miles by 7 miles.
4. Find how many minutes and seconds the storm would have
to continue to make the probability of the reservoir being
struck equal to _3_.
4
5. Explain why the measure of the central angle of a spinner is
a reliable indicator of geometric probability.
Date
Reteach
Geometric Probability
Finding Geometric Probability
–4
1.30 � 10
Use Length
Use Angle Measures
_
A point is chosen randomly on_
AD. Find the
probability that the point is on BD.
199 days 17 hours
2 minutes
2
�
4
�
_
6
�
�
all points on BD
_
P � _____________
all points on AD
0.59
Use the spinner to find
the probability of the
pointer landing on the
160° space.
1 minute 49 seconds
� _4_
9
_
A point is chosen randomly on EH. Find the
probability of each event.
_
5
�
2
�
�
2. The point is not on EF.
_3_
_3_
8
8
_
_
3. The point is on EF or GH.
4. The point is on EG.
_3_
_7_
probability.
4
8
Use the spinner to find the probability of each event.
�����
�����
1
�
_
1. The point is on FH.
circle divided by 360° equals the ratio of their areas, which is the geometric
�����
160°
160
� ____
360
_
�����
80°
120°
all points in 160� region
P � ___________________
all points in circle
BD
� ___
AD
10 � _5_
� ___
12
6
measure of the whole circle (360°). So the angle measure of a region of a
_3_
5. the pointer landing on 135�
�����
8
5
___
24
11
___
24
1
___
12
�����
6. the pointer landing on 75�
0.15
7. the pointer landing on 90� or 75�
7. Find the number of minutes and seconds the cat burglar would
have to search to have a 50% chance of finding the jewel.
8. the pointer landing on 30�
33 minutes 51 seconds
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
Holt Geometry
Class
The geometric probability of an event occurring is found by determining a ratio of
geometric measures such as length or area. Geometric probability is used when an
experiment has an infinite number of outcomes.
2
45
0.425
The theoretical probability of an event occurring is
number of outcomes in the event
P � _________________________________
.
number of outcomes in the sample space
Possible answer: A whole circle contains 360°, and its area is �r . A half
circle contains 180°, and its area is half of a whole circle, or _1_ �r 2. Therefore
2
the area of the half circle divided by the area of the whole circle is _1_, which is
2
equal to the angle measure of the half circle (180°) divided by the angle
A cat burglar plans to steal a precious jewel from the building
shown in the figure.
6. The cat burglar has not been able to find out where the jewel
is in the building. The building has two floors. He can search
50 square feet every minute, but an alarm will sound after
10 minutes. Find the probability the cat burglar will find the
jewel before the alarm sounds.
4 ft
6 ft
13. Estimate the probability that Barb will chip her ball into any hole.
Round to the nearest thousandth.
Practice C
2. Find how many days, hours, and minutes the storm would
have to continue to make the probability of the oak being
struck equal to _1_.
2
3. In the area of the storm, there is a reservoir that is roughly a
rectangle with 3-mile and 2-mile sides. Find the probability that
the reservoir will not be struck by lightning in 1 minute of the
storm. Round to the nearest hundredth.
4 ft
15. Estimate how many chip shots Barb will have to take to
ensure that one goes into a randomly selected hole.
����
1. A large oak tree in the area of the storm has a crown that is
roughly circular with a radius of 15 feet. The electrical storm
continues for 1 _1_ hours. Find the probability that the oak tree
4
will be struck by lightning during the storm. Give your answer
in scientific notation with two decimal places.
10 ft
Possible answers based on an 11.5 yd2 estimate for the green:
����
Date
135°
Barb is practicing her chip shots on the chipping green at the
local golf club. Suppose Barb’s ball drops randomly on the chipping
green. The figure shows the chipping green in a grid whose squares
have 1-yard sides. There are 18 different 4.5-inch diameter holes
on the chipping green.
180°
Find the probability that a point chosen randomly inside
the rectangle is in each given shape. Round to the
nearest hundredth.
11. the triangle
10. the trapezoid
�
65°
40°
�
0.21
0.20
0.41
0.59
9. the circle
5 times
_1_
� 120°
Find the probability that a point chosen randomly
inside the rectangle is in each given shape. Round
answers to the nearest hundredth.
2
6
_1_
3
_1_
2
_1_
2
7. the pointer landing in region D
�
3
_1_
9
59
___
72
35
___
72
5. the pointer landing in region C
6. You walk this way every day. Find the number of times the signal
will show “walk” out of 20 times that you arrive. (Hint: Find the
probability and multiply by the number of times you arrive.)
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
12
_2_
3
_
_1_
12 � _2_
___
5. Find the probability the signal will show “don’t walk” when you arrive
at the intersection.
9-6
�
7
___
Use the spinner to find the fractional probability of each event.
_
4. The point is not on RS.
The signal at a crosswalk has the following cycle: “walk” for 10 seconds,
“clear the intersection” for 10 seconds, and “don’t walk” for 20 seconds.
The figure shows the cycle represented as a line segment.
LESSON
3
�
2. The point is on BD.
1
3. The point is on AD.
4
�
_
12
_
6
5
�
5
___
�
_
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
_
1. The point is on AB.
4
6 � _1_
___
Name
Geometric Probability
�
PQ
3. The point is on RS.
18
Practice B
_
�
8
4
The point is on PQ . P � _____ � ___ � ___
18 9
PS
_
Class
A point is randomly chosen on AD. Find the
fractional probability of each event.
�
_
Date
Holt Geometry
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
61
46
30°
135°
80°
90°
75°
Holt Geometry
Holt Geometry