Answer Key
Chapter 12 – Probability 12.1
Definition of Probability
Answers 1. 4
2. One favorable outcome
3. 1/6
4. 3, 4, 5,6
5. 4 favorable outcomes
6. 4/6
7. 5, 6
8. Two favorable outcomes
9. 2/6
10. 2, 4, 6, 8, 10, 12
11. 6 favorable outcomes
12. 6:12
13. 4, 5, 6, 7, 8, 9, 10, 11, 12
14. 9 favorable outcomes
15. 9:12
16. 5
17. 5/15
18. 9
19. 9:15
20. 6
21. 6:15
22. 6
23. 6:15
24. 2
25. 2:15
12.2
Measurement of Probability
Answers 1. 9
2. One favorable outcome
3. 1:10
4. 10%
5. 3, 4
6. Two favorable outcomes
7. 10
8. 20%
9. 1, 3, 5, 7, 9
10. 5 favorable outcomes
11. 10
12. 50%
13. 6, 8, 10
14. 3
15. 10
16. 30%
17. 33.3%
18. 50%
19. 50%
20. 83.3%
12.3
Empirical Probability
Answers 1. 17
2. 60
3. 28%
4. 24
5. 50
6. 48%
7. 78
8. 100
9. 78%
10. 8
11. 40
12. 20%
13. 16
14. 50
15. 32%
CK-12 Middle School Math Concepts - Grade 7
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Answer Key
Chapter 12 – Probability 12.4
Mutually Exclusive Events
Answers 1. Overlapping
2. Disjoint
3. Disjoint
4. Overlapping
5. Disjoint
6. disjoint
7. Disjoint
8. Overlapping
9. Overlapping
10. Disjoint
11. overlapping
12. Overlapping
13. Disjoint
14. Overlapping
15. overlapping
12.5
Mutually Inclusive Events
Answers 1. 1:8
2. 3:8
3. 2:8
4. 2:8
5. 5:8
6. 2:8
7. 6:12
8. 6:12
9. 1:12
10. 1:12
11. 3:12 or 1:4
12. 6:12
13. 4:12 or 1:3
14. 5:12
15. 1:12
12.6
Complement Rule for Probability
Answers 1. .85
2. .2
3. 51%
4. 5/8
5. .93
6. .875
7. 3.9%
8. 4/5
9. Complement
10. Complement
11. Not a Complement
12 Not a Complement
13. Complement
14. Not a Complement
15. Not a complement
12.7
Counting Events
Answers 1. 6
2. 9
3. 12 options
4. 8
5. 18
6. 12
7. 36
8. 6
9. 8
10. 8
11. 10
12. 15
13. 18
14. 10
15. 14
CK-12 Middle School Math Concepts - Grade 7
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Answer Key
Chapter 12 – Probability 12.8
Sample Spaces and Events
Answers 1. 6 2. 2 3. HT
TT
4. HHH TTH
HH
TH
TTT
HTT
HTH
THH
THT
HHT
5. 3 6. 3 7. 4 8. 8 9. 12 10. 5 11. 0 12. 4 13. 4 14. True 15. False
12.9
Additive and Multiplicative Rules for Probability
Answers 1. 1/3
2. 1/3
3. 1/3
4. 1/3
5. 1/3
6. 2/3
7. 3/50
8. ½
9. ¼
10. ¼
11. 1/12
12. 1/6
13. ½
14. ¾
15. 2/3
CK-12 Middle School Math Concepts - Grade 7
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Answer Key
Chapter 12 – Probability 12.10
Basic Counting Rules
Answers 1. 6
2. 8
3. 96
4. 18
5. 8
6. 54
7. 6
8. 104
9. 84
10. 52
11. 30
12. 15
13. 10
14. 20
15. 25
12.11
Counting Rule to Calculate Probabilities
Answers 1. ¾
2. 3/8
3. ¼
4. ¼
5. ¼
6. ¼
7. 1/6
8. 1/6
9. 1/6
10. 1/6
11. 1/6
12. ½
13. ½
14. 1/3
15. 1/3
12.12
Permutations
Answers 1. Order doesn’t matter – passwords
2. Order doesn’t matter because it is trios.
3. order does matter – combination locks
4. Order does matter – prizes are given out
5. Order doesn’t matter
6. Order does matter – awards given out
7. 6
8. 24
9. 24
10. 24
11. 24
12. 120
13. 720
14. 18,060
15. 40,320 – it more than doubles
12.13
Permutation Problems
Answers 1. 6
2. 24
3. 12
4. 60
5. 120
6. 720
7. 210
8. 840
9. 120
10. 6
11. 720
12. 24
13. 12
14. 24
15. 120
16. 120
CK-12 Middle School Math Concepts - Grade 7
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Answer Key
Chapter 12 – Probability 12.14
Combinations
Answers 1. Combination
2. Combination
3. Combination
4. Permutation
5. Combination
6. Permutation
7. Combination
8. Permutation
9. Combination
10. Permutation
11. Combination
12. Combination
13. Permutation
14. Combination
15. Combination
12.15
Combination Problems
Answers 1. 120
2. 24
3. 6
4. 144,480
5. 362,880
6. 720
7. 21
8. 7
9. 70
10. 84
11. 56
12. 120
13. 220
14. 55
15. 120
12.16
Independent Events
Answers 1. Independent
2. Dependent
3. Independent
4. Independent
5. Independent
6. Dependent
7. Independent
8. Dependent
9. independent
10. Dependent
11. Dependent
12. Dependent
13. independent
14. Independent
15. Independent
CK-12 Middle School Math Concepts - Grade 7
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Answer Key
Chapter 12 – Probability 12.17
Probability of Independent Events
Answers 1. 1/9
2. 1/9
3. 2/9
4. 4/9
5. .64
6. .04
7. .16
8. 8/104
9. 3/13
10. 8/104
11. 1/8
12. 1/16
13. 1/16
14. 1/32
15. 1/32
12.18
Dependent Events
Answers 1. ¼
2. 3/8
3. ¼
4. 1/4
5. 3/8
6. 1/56
7. 3/8
8. ¼
9. 0/8
10. 3/8
11. 2/3
12. 1/5
13. 1/5
14. 3/10
15. 1/20
CK-12 Middle School Math Concepts - Grade 7
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