Answer Key
Chapter 11 – Using Probability 11.1
Using Tree Diagrams
Answers 1. 6
2. 9
3. 12
4. 8
5. 18
6. 12
7. 15
8. 18
9. 24
10. 24
11. 18
12. 18
13. 36
14. 36
15. 48
11.2
Calculating Outcomes
Answers 1. 6
2. 18
3. 6
4. 8
5. 12
6. 180
7. 360
8. No – same number
9. 9
10. 18
11. 12
12. 18
13. 1/8
14. ½
15. 6/4
11.3
Recognizing Permutations
Answers 1. 24
2. 360
3. 360
4. 40,320
5. 720
6. 24
7. 5,040
8. 60
9. 24
10. 6
11. 6
12. 24
13. 120
14. 720
15. 120
16. 5,040
11.4
Evaluating Permutations Using Permutation Notation
Answers 1. 42
2. 120
3. 120
4. 120
5. 504
6. 181,440
7. 990
8. 1,320
9. 30
10. 2, 184
11. 2,730
12. 7,920
13. 240
14. 5,040
15. 720
CK‐12 Middle School Math Concepts ‐ Grade 8
1
Answer Key
Chapter 11 – Using Probability 11.5
Recognizing Combinations
Answers 1. 15
2. 4
3. 20
4. 6
5. 210
6. 28
7. 455
8. 126
9. 10
10. 3
11. 6
12. 4
13. 10
14. 10
15. 5
11.6
Evaluating Combinations Using Combination Notation
Answers 1. 10
2. 6
3. 21
4. 35
5. 28
6. 15
7. 36
8. 126
9. 56
10. 1
11. 10
12. 10
13. 15
14. 20
15. 35
16. 45
11.7
Theoretical Probability
Answers 1. a.
blue
b. 1 out of 5
c. 5
d. 1:5
2. a.
red, green
b. 2 out of 5
c. 5
d. 2:5
c. 5
d. 4:5
3. a. purple, green, red, blue
b. 4 out of 5
4. a. 3, 4
b. 2
c. 6
d. 2:6 or 1:3
5. a. 3, 4, 5, 6
b. 4
c. 6
d. 4:6 or 2:3
11.8
Experimental Probability
Answers 1. 1, 2, 3
2. 3
3. 6
4. 3:6 or 1:2
5. 1, 6
6. 2
7. 6
8. 2:6 or 1:3
9. 1, 2, 3
10. 3
11. 12
12. 3:12 or 1:4
13. 31
14. 60
15. 31:60
CK‐12 Middle School Math Concepts ‐ Grade 8
2
Answer Key
Chapter 11 – Using Probability 11.9
Write and Compare Probabilities as Fractions, Decimals and Percents
Answers 1. 6/25
2. .24
3. 24%
4. 5/25 = 1/5
5. .2
6. 20%
7. 7/25
8. 2/25
9. .28
10. 12/25
11. 5/25 = 1/5
12. .2
13. 20%
14. Red, green, white
15. blue, yellow, white
16. Red, blue, green
11.10
Identify Overlapping, Disjoint and Complementary Events
Answers 1. Disjoint
2. Complementary
3. They depend on each other.
4. Disjoint
5. Even numbers don’t include 3
6. Overlapping
7. Overlapping
8. Complementary
9. Disjoint
10. Overlapping
11. Complementary
12. Complementary
13. Disjoint
14. Complementary
15. Disjoint
11.11
Calculate Odds Using Outcomes or Probability
Answers 1. 1:5
2. 4:5
3. 3:3
4. 4:2
5. 2:4
6. 3:3
7. 3:3
8. 1:9
9. 2:8
10. 3:7
11. 5:5
12. 9:1
13. 8:2
14. 2:8
15. 3:7
11.12
Recognize Independent and Dependent Events
Answers 1. Independent
2. Dependent
3. Independent
4. Independent
5. Dependent
6. Dependent
7. Dependent
8. Independent
9. Dependent
10. Dependent
11. Independent
12. Dependent
13. Independent
14. Independent
15. Independent
CK‐12 Middle School Math Concepts ‐ Grade 8
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Answer Key
Chapter 11 – Using Probability 11.13
Understanding Conditional Probability
Answers 1. 1/11
2. 4/33
3. 3/165
4. 3/14
5. 2/7
6. 7/30
7. 1/10
8. 1/40
9. 1/3
10. ½
11. 2/3
12. 1/36
13. 1/12
14. 1/18
15. 5/6
11.14
Understanding Geometric Probability
Answers 1. 12.5%
2. 25%
3. 31.25%
4. 34.4%
5. 7 miles
6. 16.7%
7. 25%
8. 8%
9. 83%
10. 20%
11. 40%
12. 60%
13. 80%
14. 100%
15. 60%
16. 40%
11.15
Use Simulations to Explore Experimental Probability
Answers Answers will vary based on experiments.
CK‐12 Middle School Math Concepts ‐ Grade 8
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