Name———————————————————————— Date —————————————
Practice B
Lesson
11.4
For use with the lesson “Use Geometric Probability”
Lesson 11.4
}
Find the probability that a point K, selected randomly on AE​
​  , is on the
given segment. Express your answer as a fraction, decimal, and percent.
A
B
−8
−6
C
−4
−2
D
0
}
2
E
4
6
8
}
}
1.​BC​ 
2. ​BD​ 
}
3.​CE​ 
4. ​AD​ 
Find the probability that a randomly chosen point in the figure lies in the
shaded region.
5.
6.
6
6
6
8
10
8.
7.
2
6
9.
10.
7
12
4
Find the probability that a point chosen at random on the segment
satisfies the inequality.
1
2
3
4
11. x 1 3 ≤ 5
5
6
7
8
12. 2x 2 3 ≤ 3
9
13. 3x 1 5 ≥ 17
14. 2x 2 12 ≥ 8
Use the scale drawing.
15. What is the approximate area of the shaded figure
in the scale drawing?
16. Find the probability that a randomly chosen point
lies in the shaded region.
17. Find the probability that a randomly chosen point
lies outside of the shaded region.
18. Boxes and Buckets A circular bucket with a diameter of 18 inches is placed inside
a two foot cubic box. A small ball is thrown into the box. Find the probability that
the ball lands in the bucket.
11-50
Geometry
Chapter Resource Book
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
8
16
Name———————————————————————— Lesson
11.4
Date —————————————
Practice B continued
For use with the lesson “Use Geometric Probability”
Arcs and Sectors The figure to the right shows a circle with a sector that intercepts an arc of 60°.
Lesson 11.4
In Exercises 19 and 20, use the following information.
60°
19. Find the probability that a randomly chosen point on
the circle lies on the arc.
20. Find the probability that a randomly chosen point in the
circle lies in the sector.
Find the probability that a randomly chosen point in the figure lies in the
shaded region.
21.
22.
8
12
4
2
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
region A, and A includes region B and region C.
What is the probability that X is not in B?
Area of A 1 Area
of C
A.​ }}
  
 ​
  
Area of A
Area of A 1 Area of C 2 Area of B
B. }}}
​ 
   
   
 ​
Area of A 1 Area of C
Area of A 2 Area of B
C. }}
​ 
  
 ​
  
Area of A
6
4
24. Multiple Choice A point X is chosen at random in 23.
1.5
A
B
C
25. Subway At the local subway station, a subway train is scheduled to arrive every
15 minutes. The train waits for 2 minutes while passengers get off and on, and then
departs for the next station. What is the probability that there is a train waiting when
a pedestrian arrives at the station at a random time?
In Exercises 26–28, use the following information.
School Day The school day consists of six block classes with each being 60 minutes long.
Lunch is 25 minutes. Transfer time between classes and/or lunch is 3 minutes. There is a
fire drill scheduled to happen at a random time during the day.
26. What is the probability that the fire drill begins during lunch?
27. What is the probability that the fire drill begins during transfer time?
28. If you are 2 hours late to school, what is the probability that you missed the
fire drill?
Geometry
Chapter Resource Book
11-51
Lesson 11.3 Areas of Regular
Polygons, continued
25. about 13.3% 26. about 6.2%
legs r and r.}Therefore, the radius of the larger
circle is r​Ï2 ​.  The ratio of the area of the smaller
Practice Level C
5
1
1. }
​ 8 ​ ; 0.625; 62.5% 2. }
​ 2 ​ ; 0.5; 50%
3
3
3. ​ } ​ ; 0.375; 37.5% 4. }
​ 4  ​; 0.75; 75% 5. 62.5%
8
π r 2
π r 2
1
circle to the larger circle is ​ }
5}
​  2   ​ 5 }
​ 2 ​ .
}   ​ 
2
6. Equilateral triangle: 1924.5 ft2; square:
2500 ft2; regular pentagon: 2752.8 ft2; regular
hexagon: 2886.8 ft2; circle: 3183.1 ft2; The farmer
should choose a circle.
9. about 17.3% 10. about 20.3% 11. 75%
12. 50% 13. 25% 14. 56.25% 15. 37.5%
Lesson 11.4 Use Geometric
Probability
16. 93.75% 17. 35 18. about 19.9%
Teaching Guide
22. about 31.83% 23. about 75.68%
1. Answers may vary but most students will pick
sector A because it is most likely to occur.
2. Answers may vary but most students will pick
sector D because it is least likely to occur.
5
1
3. }
​ 6 ​ 4. }
​ 24  ​
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
6. 68.75% 7. 62.5% 8. about 21.46%
Practice Level A
3
1
1. }
​ 2 ​ ; 0.5; 50% 2. }
​ 8 ​ ; 0.375; 37.5%
3
1
3. }
​ 4  ​; 0.25; 25% 4. ​ }4  ​; 0.75; 75% 5. 50%
6. about 21.46% 7. about 36.3% 8. 80%
9. 75% 10. about 17.65% 11. 50% 12. 25%
13. 37.5% 14. 75% 15. 70 square units
16. about 39.8% 17. about 60.2% 18. 25%
19. 25% 20. about 47.64% 21. 25% 22. 32%
23. C 24. 25% 25. about 38.9%
26. about 8.3% 27. about 19.4%
28. about 8.3% 29. 10% 30. about 6.4%
Practice Level B
3
5
1. }
​ 8 ​; 0.375; 37.5% 2. ​ }8 ​; 0.625; 62.5%
3
1
3. }
​ 2 ​; 0.5; 50% 4. ​ }4 ​; 0.75; 75% 5. about 47.6%
6. 68.75% 7. 25% 8. 25% 9. about 56.95%
10. about 17.3% 11. 12.5% 12. 25%
13. 62.5% 14. 0% 15. 49.5 16. about 28.1%
17. about 71.9% 18. about 44.2%
19. about 16.7% 20. about 16.7%
21. about 78.5% 22. 32% 23. 50% 24. C
answers
π r 2
π (r​Ï2 ​ )
27. about 4.5% 28. about 29.8%
19. about 80.1% 20. 47.5% 21. 47.5%
24. about 57.8% 25. 20% 26. 25%
27. a. 6.25% b. 18.75% c. 31.25% d. 43.75%
Study Guide
3
1
1. }
​ 8 ​ 5 0.375 5 37.5% 2. }
​   ​  5 0.125 5 12.5%
8
5
1
3. }
​ 2 ​ 5 0.5 5 50% 4. }
​ 8 ​ 5 0.625 5 62.5%
5. 18.75% 6. 25.37% 7. 45%
Problem Solving Workshop:
Mixed Problem Solving
1. a. 20% b. 80% 2. a. 15 in., 10 in.
b. about 47.12 in., about 31.42 in. c. about 8.49
revolutions, about 12.73 revolutions
3. a. about 1.3% b. 4; The probability of a
1
marker landing in the target region is }
​ 75  ​ . Solve
x
1
the proportion }
​ 300   ​ 5 }
​ 75  ​ to find the number x of
markers out of 300 that you would expect to land
in the target region. 4. about 46
5. 132.73 in.2, 40.84 in.; 530.93 in.2, 81.68 in.;
Doubling the radius quadruples the area of the
circle because you are substituting 2r for r in the
equation for the area of a circle. Doubling the
radius doubles the circumference because you
are substituting 2r for r in the equation for the
­circumference of a circle. 6. Answers will vary.
7. a. about 494.8 mi b. 9.63 mi; The distance
the boat travels in the beam of light is a chord
of the circle. The chord that is the perpendicular
bisector of this chord is the diameter of the circle.
So, you can find the center of the circle, which
is the lighthouse. The distance from the center
along the diameter to the chord is the shortest distance because the shortest distance between a
Geometry
Chapter Resource Book
A61