1. 15.1 – Presenting Statistical Data
HW: Page , 1-15 all

2. 1. Draw a stem-and-leaf plot for the given distribution.
16, 54, 23, 38, 22, 22, 40, 46, 52, 19, 20 16, 19, 20, 22, 22, 23, 38, 40, 46, 52, 54 1 2 3 4 5
6, 9
0, 2, 2, 3 8
0, 6
2, 4

3. 3. Draw a stem-and-leaf plot for the given distribution.
2, 5, 13, 28, 61, 9, 18, 10, 52, 34, 28, 42, 19, 28, 7 2, 5, 7, 9, 10, 13, 18, 19, 28, 28, 28, 34, 42, 52, 61 1 2 3 4 5 6
2, 5, 7, 9
0, 3, 8, 9
8, 8, 8

4. 5a) Find the mode of the distribution
16, 54, 23, 38, 22, 22, 40, 46, 52, 19, 20 16, 19, 20, 22, 22, 23, 38, 40, 46, 52, 54 Mode (most frequent) = 22

5. 5b) Find the median of the distribution
16, 54, 23, 38, 22, 22, 40, 46, 52, 19, 20 16, 19, 20, 22, 22, 23, 38, 40, 46, 52, 54

6. 5c) Find the mean of the distribution
16, 54, 23, 38, 22, 22, 40, 46, 52, 19,

7. 7a) Find the mode of the distribution
2, 5, 13, 28, 61, 9, 18, 10, 52, 34, 28, 42, 19, 28, 7 2, 5, 7, 9, 10, 13, 18, 19, 28, 28, 28, 34, 42, 52, 61 Mode (most frequent) = 28

8. 7b) Find the median of the distribution

9. 7c) Find the mean of the distribution
2, 5, 13, 28, 61, 9, 18, 10, 52, 34, 28, 42, 19, 28, 7 2, 5, 7, 9, 10, 13, 18, 19, 28, 28, 28, 34, 42, 52,

10. 9. The frequency distribution of the heights of the members of a high school basketball team is shown. Find (a) the mode, (b) median, and (c) the mean
Height (cm)
Frequency
175 1
178
180 2
181
184 3
185
188
192
175, 178, 180, 180, 181, 184, 184, 184, 185, 185, 188, 192
Mode: 184
Median: 184
Mean:
Mean: 183

11. 11. Draw a histogram for the frequency distribution of quiz scores shown at the right.10 2 15 5 20 8 25 30

12. 13. James has test scores of 82, 73, 76, and 92
13. James has test scores of 82, 73, 76, and 92. What must he score on a fifth test if his average test score is to be 82?
𝑥 5 = 𝑥 5 = 𝑥 =410 𝑥=87

13. 15. If each score in a set of scores were increased by 5 points, how would this affect the mode, median, and mean of these scores?
2, 3, 4, 4, 5 Mean = = 4 Median = 4 Mode = 4
7, 8, 9, 9, 10
Mean =
= 9
Median = 9
Mode = 9

14. 17. At high school A, the mean score of 50 students on a science test is 75. At high school B, the mean score of 40 students on the same test is 80. What is the mean score of the 90 students?
𝑥 50 =75 𝑥=3,750
𝑥 40 =80
𝑥=3200
Average = 6,950 90
77.2

15. 15.2 – Analyzing Statistical Data
HW: Oral Exercises, 1-14 all

16. 1. Find the median 1
0, 0, 5, 6 2
0, 4, 5, 5, 5, 5, 7, 9 3
7, 8, 9, 9, 9
10, 10, 15, 16, 20, 24, 25, 25, 25, 25, 27, 29, 37, 38, 39, 39, 39 Median = 25

17. 2. Find the first quartile1
0, 0, 5, 6 2
0, 4, 5, 5, 5, 5, 7, 9 3
7, 8, 9, 9, 9
10, 10, 15, 16, 20, 24, 25, 25, 25, 25, 27, 29, 37, 38, 39, 39, 39
Median = 20

18. 3. Find the third quartile1
0, 0, 5, 6 2
0, 4, 5, 5, 5, 5, 7, 9 3
7, 8, 9, 9, 9
10, 10, 15, 16, 20, 24, 25, 25, 25, 25, 27, 29, 37, 38, 39, 39, 39 Third Quartile = 37

19. 4. Find the range 1
0, 0, 5, 6 2
0, 4, 5, 5, 5, 5, 7, 9 3
7, 8, 9, 9, 9
10, 10, 15, 16, 20, 24, 25, 25, 25, 25, 27, 29, 37, 38, 39, 39, 39 Range = 39−10 Range = 29

20. 5. Use the box-and-whisker plot to state what each of the following points represents and to give its value.
A Lowest Value B First Quartile C Median D Third Quartile E Highest Value 50 60 70 80 90
100 A B C D E

21. 6. Which class has the highest score?60 70 80 90
100
Class 1
Class 2

22. 7. Which class has the lowest score?60 70 80 90
100
Class 1
Class 2

23. 8. Which class has the smaller range?
Same 60 70 80 90
100
Class 1
Class 2

24. 9. Which class has the higher median?60 70 80 90
100
Class 1
Class 2

25. 10. Which class has the highest first quartile?60 70 80 90
100
Class 1
Class 2

26. 11. Which class has the higher third quartile?60 70 80 90
100
Class 1
Class 2

27. 12. Which class has scores in the middle half closer together?60 70 80 90
100
Class 1
Class 2

28. 13. Which class has the better set of scores?60 70 80 90
100
Class 1
Class 2

29. The data in distribution A is more spread out from the mean.
14. What can you say about distributions A and B if they have the same mean but the standard deviation of A is greater than that of B? 60 70 80 90
100
The data in distribution A is more spread out from the mean.
Class 1
Class 2

30. 15.2 – Analyzing Statistical Data
HW: Written Ex. Page 717, 1-15 all

31. 1a. Find the median
2, 3, 7, 10, 14, 14, 18, 22, 25, 25, 25, 29, 29, 30, 34, 34, 38, 38, 40, 41, 47
2, 3, 7 1
0, 4, 4, 8 2
2, 5, 5, 5, 9, 9 3
0, 4, 4, 8, 8 4
0, 1, 7
Median = 25

32. 1b. Find the first quartile
2, 3, 7, 10, 14, 14, 18, 22, 25, 25, 25, 29, 29, 30, 34, 34, 38, 38, 40, 41, 47
2, 3, 7 1
0, 4, 4, 8 2
2, 5, 5, 5, 9, 9 3
0, 4, 4, 8, 8 4
0, 1, 7
First Quartile = 14

33. 1c. Find the third quartile
2, 3, 7, 10, 14, 14, 18, 22, 25, 25, 25, 29, 29, 30, 34, 34, 38, 38, 40, 41, 47
2, 3, 7 1
0, 4, 4, 8 2
2, 5, 5, 5, 9, 9 3
0, 4, 4, 8, 8 4
0, 1, 7
Third Quartile: 34

34. 1d. Find the range
2, 3, 7, 10, 14, 14, 18, 22, 25, 25, 25, 29, 29, 30, 34, 34, 38, 38, 40, 41, 47
2, 3, 7 1
0, 4, 4, 8 2
2, 5, 5, 5, 9, 9 3
0, 4, 4, 8, 8 4
0, 1, 7
Range = 47−2
= 45

35. 2a. Find the median
59, 63, 63, 67, 71, 76, 76, 76, 80, 80, 84, 84, 88, 92, 95, 95 5 9 6
3, 3, 7 7
1, 6, 6, 6 8
0, 0, 4, 4, 8
2, 5, 5
Median =
Median =
Median = 78

36. 2b. Find the first quartile
59, 63, 63, 67, 71, 76, 76, 76, 80, 80, 84, 84, 88, 92, 95, 95 5 9 6
3, 3, 7 7
1, 6, 6, 6 8
0, 0, 4, 4, 8
2, 5, 5
First Quartile:
First Quartile:
First Quartile: 69

37. 2b. Find the third quartile
59, 63, 63, 67, 71, 76, 76, 76, 80, 80, 84, 84, 88, 92, 95, 95 5 9 6
3, 3, 7 7
1, 6, 6, 6 8
0, 0, 4, 4, 8
2, 5, 5
Third Quartile:
Third Quartile:
Third Quartile: 86

38. 2d. Find the range
59, 63, 63, 67, 71, 76, 76, 76, 80, 80, 84, 84, 88, 92, 95, 95 5 9 6
3, 3, 7 7
1, 6, 6, 6 8
0, 0, 4, 4, 8
2, 5, 5
Range: 95−59
Range: 36

39. 3. Make a box-and-whisker plot for question 1
Lowest Number: 2 First Quartile: 14 Median: 25 Third Quartile: 34 Highest Number: 47 10 20 30 40 50 A B C D E

40. 4. Make a box-and-whisker plot for question 2
Lowest Number: 59 First Quartile: 69 Median: 78 Third Quartile: 86 Highest Number: 95 50 60 70 80 90
100 A B C D E

41. 5. Which class has the highest median?60 70 80 90
100
Class 1
Class 2
Class 3

42. 6. Which class has the smallest range?60 70 80 90
100
Class 1
Class 2
Class 3

43. 7. For which class are the scores in the middle half closest together?60 70 80 90
100
Class 1
Class 2
Class 3

44. 8. Which class has the best set of scores?60 70 80 90
100
Class 1
Class 2
Class 3

45. 9a. Find the mean
1, 4, 6, 6, 7, 8, 8,

46. 9b. Find the variance Deviations (𝐃𝐞𝐯𝐢𝐚𝐭𝐢𝐨𝐧 𝐬) 𝟐 5 25 2 4 11
1, 4, 6, 6, 7, 8, 8, 8 Mean =

47. 9c. Find the standard deviation
1, 4, 6, 6, 7, 8, 8, 8 Variance = 5.25 Standard Deviation = 5.25 Standard Deviation = 2.9

48. 10a. Find the mean
3, 4, 5, 5, 5, 6,

49. 10b. Find the variance Deviations (𝐃𝐞𝐯𝐢𝐚𝐭𝐢𝐨𝐧 𝐬) 𝟐 2.3 5.29 1.3 1.69 .3
.09 .7
.49
3.7
13.69
3, 4, 5, 5, 5, 5, 6, 9 Mean =

50. 10c. Find the standard deviation
3, 4, 5, 5, 5, 6, 9 Variance = 2.7 Standard Deviation = 2.7 Standard Deviation = 1.6

51. 11a. Find the mean
34, 42, 44, 70, 73,

52. 11b. Find the variance
Deviations
(𝐃𝐞𝐯𝐢𝐚𝐭𝐢𝐨𝐧 𝐬) 𝟐
22.7
515.3
14.67
215.1
12.67
160.4
13.33
177.7
16.33
266.8
22.33
498.8
34, 42, 44, 70, 73, 79 Mean = 56.7 Variance = Variance = 305.4

53. 11c. Find the standard deviation
34, 42, 44, 70, 73, 79 Variance = Standard Deviation = Standard Deviation = 17.5

54. 12a. Find the mean
8, 15, 38, 64, 85,

55. 12b. Find the variance
Deviations
(𝐃𝐞𝐯𝐢𝐚𝐭𝐢𝐨𝐧 𝐬) 𝟐 44
1936 37
1369 14
196 12
144 33
1089 50
2500
8, 15, 38, 64, 85, 102 Mean = Variance =

56. 12c. Find the standard deviation
8, 15, 38, 64, 85, 102 Variance = Standard Deviation = Standard Deviation = 34.7

57. 13a. Find the mean
42, 46, 50, 50, 52, 54, 56 50

58. 13b. Find the variance 100+36+4+4+0+4+16 7 42, 46, 50, 50, 52, 54, 56
Deviations
(𝐃𝐞𝐯𝐢𝐚𝐭𝐢𝐨𝐧 𝐬) 𝟐 10
100 6 36 2 4 16
42, 46, 50, 50, 52, 54, 56
Mean = 52
19.4

59. 13c. Find the standard deviation
42, 46, 50, 50, 52, 54, 56 Variance = 19.4 Standard Deviation = 19.4 Standard Deviation = 4.4

60. 14a. Find the mean
37, 38, 41, 45, 45, 47,

61. 14b. Find the variance
Deviations
(𝐃𝐞𝐯𝐢𝐚𝐭𝐢𝐨𝐧 𝐬) 𝟐 6 36 5 25 2 4 16
37, 38, 41, 45, 45, 47, 48 Mean = 43 Variance = Variance = 16.3

62. 14c. Find the standard deviation
37, 38, 41, 45, 45, 47, 48 Variance = 16.3 Standard Deviation = 16.3 Standard Deviation = 4.0

63. 15a. In a golf tournament the 18-hole totals for the top nine golfers were 67, 69, 70, 70, 71, 72, 73, 73, and 74. Find the mean. 71

64. 15b. In a golf tournament the 18-hole totals for the top nine golfers were 67, 69, 70, 70, 71, 72, 73, 73, and 74. Find the variance
Deviations
(𝐃𝐞𝐯𝐢𝐚𝐭𝐢𝐨𝐧 𝐬) 𝟐 4 16 2 1 3 9
Mean = 71
4.4

65. 15c. In a golf tournament the 18-hole totals for the top nine golfers were 67, 69, 70, 70, 71, 72, 73, 73, and 74. Find the standard deviation.
Variance = 4.4
Standard Deviation = 4.4
Standard Deviation = 2.1

66. 15.3 – The Normal Distribution
HW: Page 722, 1-7 all

67. 1. In a standard normal distribution, what percent of the data is between the mean and 0.4?X
Area, A(x)
0.0
0.0000
0.2
0.0793
0.4
0.1554
.1554
15.54%

68. 2. In a standard normal distribution, what percent of the data is between -0.2 and 0.2?X
Area, A(x)
0.0
0.0000
0.2
0.0793
0.4
0.1554
.1586
15.86%

69. 3. In a standard normal distribution, what percent of the data is between three and four standard deviations below the mean? X
Area, A(x)
3.0
.4978
4.0
.5000
.0013
.13%

70. 4. In a standard normal distribution, what percent of the data is within three standard deviations from the mean? X
Area, A(x)
3.0
.4978
49.78%

71. 𝑧= number you are converting 𝑀= mean 𝜎= standard deviation .5000−.3413
5a . The mean weight of a loaf of bread was found by sampling to be 455 g, with a standard deviation of 5 g. Assuming a normal distribution, find the percent of loaves with weights that are less than 450 g.
𝑥= 𝑧−𝑀 𝜎
𝑥= 450−455 5
𝑥=− 5 5
𝑥=−1
𝑧= number you are converting
𝑀= mean
𝜎= standard deviation
.5000−.3413
.1587
15.87%
What percentage is less than -1 ? X
Area, A(x)
1.0
.3413

72. 𝑧= number you are converting 𝑀= mean 𝜎= standard deviation .5000+.4772
5b . The mean weight of a loaf of bread was found by sampling to be 455 g, with a standard deviation of 5 g. Assuming a normal distribution, find the percent of loaves with weights that are greater than 445 g.
𝑥= 𝑧−𝑀 𝜎
𝑥= 445−455 5
𝑥= −10 5
𝑥=−2
𝑧= number you are converting
𝑀= mean
𝜎= standard deviation
.9772
97.72%
What percentage is greater than -2 ? X
Area, A(x)
2.0
.4772

73. 𝑧= number you are converting 𝑀= mean 𝜎= standard deviation .5000−.4987
5c . The mean weight of a loaf of bread was found by sampling to be 455 g, with a standard deviation of 5 g. Assuming a normal distribution, find the percent of loaves with weights that are greater than 470 g.
𝑥= 𝑧−𝑀 𝜎
𝑥= 470−455 5
𝑥= 15 5
𝑥=3
𝑧= number you are converting
𝑀= mean
𝜎= standard deviation
.5000−.4987
.0013
.13%
What percentage is greater than 3 ? X
Area, A(x)
3.0
.4987

74. 𝑧= number you are converting 𝑀= mean 𝜎= standard deviation
5d . The mean weight of a loaf of bread was found by sampling to be 455 g, with a standard deviation of 5 g. Assuming a normal distribution, find the percent of loaves with weights that are between 450 g and 460 g.
𝑥= 𝑧−𝑀 𝜎
𝑥= 450−455 5
𝑥= −5 5
𝑥=−1
𝑥= 𝑧−𝑀 𝜎
𝑥= 460−455 5
𝑥= 5 5
𝑥=1
𝑧= number you are converting
𝑀= mean
𝜎= standard deviation
What percentage is between -1 and 1?
.6826
68.26% X
Area, A(x)
1.0
.3413

75. 𝑧= number you are converting 𝑀= mean 𝜎= standard deviation .5000−.4987
6a. A college aptitude test is scaled so that its scores approximate a normal distribution with a mean of 500 and a standard deviation of 100. Find the percent of the students taking the test who are expected to score above 800 points.
𝑥= 𝑧−𝑀 𝜎
𝑥= 800− 𝑥=
𝑥=3
𝑧= number you are converting
𝑀= mean
𝜎= standard deviation
.5000−.4987
.0013
.13%
What percentage is greater than 3 ? X
Area, A(x)
3.0
.4987

76. 𝑧= number you are converting 𝑀= mean 𝜎= standard deviation .5000−.3413
6b. A college aptitude test is scaled so that its scores approximate a normal distribution with a mean of 500 and a standard deviation of 100. Find the percent of the students taking the test who are expected to score less than 400 points.
𝑥= 𝑧−𝑀 𝜎
𝑥= 400−
𝑥= −
𝑥=−1
𝑧= number you are converting
𝑀= mean
𝜎= standard deviation
.5000−.3413
.1587
15.87%
What percentage is less than -1 ? X
Area, A(x)
1.0
.3413

77. 𝑧= number you are converting 𝑀= mean 𝜎= standard deviation
6c. A college aptitude test is scaled so that its scores approximate a normal distribution with a mean of 500 and a standard deviation of 100. Find the percent of the students taking the test who are expected to score between 700 and 900 points.
𝑥= 𝑧−𝑀 𝜎
𝑥= 700− 𝑥=
𝑥=2
𝑥= 𝑧−𝑀 𝜎
𝑥= 900− 𝑥=
𝑥=4
𝑧= number you are converting
𝑀= mean
𝜎= standard deviation
What percentage is between -1 and 1?
.5000−.4772
.0228
2.28% X
Area, A(x)
2.0
.4772
4.0
.5000

78. 𝑧= number you are converting 𝑀= mean 𝜎= standard deviation
6d. A college aptitude test is scaled so that its scores approximate a normal distribution with a mean of 500 and a standard deviation of 100. Find the percent of the students taking the test who are expected to score between 800 and 820 points.
𝑥= 𝑧−𝑀 𝜎
𝑥= 800− 𝑥=
𝑥=3
𝑥= 𝑧−𝑀 𝜎
𝑥= 820− 𝑥=
𝑥=3.2
𝑧= number you are converting
𝑀= mean
𝜎= standard deviation
What percentage is between -1 and 1?
.4993−.4987
.0006
.06% X
Area, A(x)
3.0
.4987
3.2
.4993

79. 𝑧= number you are converting 𝑀= mean 𝜎= standard deviation .5000
7a. The mean life of a certain kind of light bulb is 900 h with a standard deviation of 30 h. assuming the lives of the light bulbs are normally distributed, find the percent of the light bulbs that will last less than 900 h.
𝑥= 𝑧−𝑀 𝜎
𝑥= 900−900 30
𝑥= 0 30
𝑥=0
𝑧= number you are converting
𝑀= mean
𝜎= standard deviation
.5000
What percentage is less than 0 ?

80. 𝑧= number you are converting 𝑀= mean 𝜎= standard deviation .5000−.4974
7b. The mean life of a certain kind of light bulb is 900 h with a standard deviation of 30 h. assuming the lives of the light bulbs are normally distributed, find the percent of the light bulbs that will last more than 984 h.
𝑥= 𝑧−𝑀 𝜎
𝑥= 984−900 30
𝑥= 84 30
𝑥=2.8
𝑧= number you are converting
𝑀= mean
𝜎= standard deviation
.5000−.4974
.0026
.26%
What percentage is more than 2.8 ? X
Area, A(x)
2.8
.4974

81. Correlation
Page 727, Oral Ex. 1-3 all

82. 1a. When two variables have a high _______ correlation, one variable increases as the other variable increases. Positive

83. 1b. When two variables have a high _______ correlation, one variable decreases as the other variable increases. Negative

84. 2a. If the correlation coefficient, 𝑟 𝑥𝑦 =0
2a. If the correlation coefficient, 𝑟 𝑥𝑦 =0.05, is the linear relationship between x and y strong or weak? Weak Because the coefficient is closer to 0 than to 1

85. 2b. If the correlation coefficient, 𝑟 𝑥𝑦 =−0
2b. If the correlation coefficient, 𝑟 𝑥𝑦 =−0.95, is the linear relationship between x and y strong or weak? Strong Because the coefficient is closer to -1 than to 0

86. 2c. If the correlation coefficient, 𝑟 𝑥𝑦 =−0
2c. If the correlation coefficient, 𝑟 𝑥𝑦 =−0.10, is the linear relationship between x and y strong or weak? Weak Because the coefficient is closer to 0 than to -1

87. 2d. If the correlation coefficient, 𝑟 𝑥𝑦 =0
2d. If the correlation coefficient, 𝑟 𝑥𝑦 =0.90, is the linear relationship between x and y strong or weak? Strong Because the coefficient is closer to 1 than to 0

88. 3a. Is there positive, negative, or close to zero correlation between a high school student’s height and weight? Positive Because as height increases, weight also increases

89. 3b. Is there positive, negative, or close to zero correlation between a car’s age and its value? Negative Car’s age increases and value decreases (ignoring very old cars)

90. 3c. Is there positive, negative, or close to zero correlation between a team’s standing in its conference and the attendance at its games. Positive Higher standing (better team), more people will want to attend

91. 3d. Is there positive, negative, or close to zero correlation between a state’s monthly temperature averages and precipitation totals? Close to zero It rains during any temperature

92. 3e. Is there positive, negative, or close to zero correlation between a company’s advertising budget and its volume of sales? Positive More advertisement, more sales

93. 15.5 – Fundamental Counting Principles
HW: Page 732, 1-13 all

94. 4 x 5 How many even 2-digit positive integers less than 50 are there?
# of Choices _____ _____
Digit Digit 2
20 integers

95. 2. How many odd 2-digit positive integers greater than 20 are there?x 5
# of Choices _____ _____
Digit Digit 2
40 integers

96. 5 x 5 x 2 # of Choices _____ _____ _____ Digit 1 Digit 2 Digit 3
3. How many odd 3-digit positive integers can be written using the digits 2, 3, 4, 5, and 6? x x 2
# of Choices _____ _____ _____
Digit Digit 2 Digit 3
50 integers

97. 5 x 5 x 3 # of Choices _____ _____ _____ Digit 1 Digit 2 Digit 3
4. How many even 3-digit positive integers can be written using the digits 1, 2, 4, 7, and 8? x x 3
# of Choices _____ _____ _____
Digit Digit 2 Digit 3
75 integers

98. 8 x 5 x 3 # of Choices _____ _____ _____ Alg. Geo. Calc.
5. In how many ways can you select one algebra book, one geometry book, and one calculus book from a collection of 8 different algebra books, 5 different geometry books, and 3 different calculus books. x x 3
# of Choices _____ _____ _____
Alg. Geo. Calc.
120 ways to select

99. 5 x 4 x 3 x 2 # of Choices _____ _____ _____ _____
6. A student council has 5 seniors, 4 juniors, 3 sophomores, and 2 freshmen as members. In how many ways can a 4-member council committee be formed that includes one member of each class? x x
3 x 2
# of Choices _____ _____ _____ _____
Seniors Juniors Soph. Fresh.
120 ways to select

100. 7. In how many different ways can a 10-question true-false test be answered if every question must be answered.
Q1: 2 options
Q2: 2 options
Q3: 2 options .
Q10: 2 options
2∙2∙2∙2∙2∙2∙2∙2∙2∙2
1024 ways to answer

101. 8. In how many different ways can a 10-question true-false test be answered if it is all right to leave questions unanswered?
Q1: 3 options
Q2: 3 options
Q3: 3 options .
Q10: 3 options
3∙3∙3∙3∙3∙3∙3∙3∙3∙3
59,049 ways to answer

102. 9. How many ways are there to select 3 cards, one after the other, from a deck of 52 cards if the cards are not returned to the deck after being selected?
Card 1: 52 options
Card 2: 51 options
Card 3: 50 options
52∙51∙50
132,600

103. 10. How many ways are there to write a 3-digit positive integer using the digits 1, 3, 5, 7, and 9 if no digit is to be used more than once?
1st digit: 5 options
2nd digit: 4 options
3rd digit: 3 options
5∙4∙3
60 ways

104. 11. How many 7-digit telephone numbers can be created if the first digit must be 8, the second number must be 5, and the third must be 2 or 3?
1st digit: 1 option
2nd digit: 1 option
3rd digit: 2 options
4th digit: 10 options
5th digit: 10 options
6th digit: 10 options
7th digit: 10 options
1∙1∙2∙10∙10∙10∙10
20,000 telephone numbers

105. 12. How many positive odd integers less than 10,000 can be written using the digits 3, 4, 6, 8, and 0?
1st digit: 5 options
2nd digit: 5 options
3rd digit: 5 options
4th digit: 1 option
5∙5∙5
125 integers

106. 13. How many license plates of 3 symbols (letters and digits) can be made using at least 2 letters for each.
2 letters
Letter 1: 26 options
Letter 2: 26 options
Digit 1: 10 options
26∙26∙10
6,760
2 letters
Letter 1: 26 options
Digit 1: 10 options
Letter 2: 26 options
26∙10∙26
6,760
2 letters
Digit 1: 10 options
Letter 1: 26 options
Letter 2: 26 options
26∙10∙26
6,760
3 letters
Letter 1: 26 options
Letter 2: 26 options
Letter 3: 26 options
26∙26∙26
17,576
Total Rearrangements: 6,760+6,760+6,760+17,576
Total Rearrangements: 37,856

107. Permutations
HW: Page 737, 1-21 all

108. Evaluate 3!5!
3∙2∙1∙5∙4∙3∙2∙1
720

109. 3. Evaluate 8! 8−3 !
8∙7∙6∙5∙4∙3∙2∙1 5∙4∙3∙2∙1
336

110. 5. Find nPr if 𝑛=7, 𝑟=7 7P7 = 7! 7−7 ! 7∙6∙5∙4∙3∙2∙1 5040

111. 7. Find nPr if 𝑛=6, 𝑟=1 6P1 = 6! 6−1 ! 6∙5∙4∙3∙2∙1 5∙4∙3∙2∙1 6

112. 9. In how many ways can 6 different books be arranged on a shelf
9. In how many ways can 6 different books be arranged on a shelf? 1st spot: 6 options 2nd spot: 5 options 3rd spot: 4 options 4th spot: 3 options 5th spot: 2 options 6th spot: 1 option
6∙5∙4∙3∙2∙1
720

113. 11. In how many ways can 3 cards from a deck of 52 cards be laid in a row face up? Card 1: 52 options Card 2: 51 options Card 3: 50 options
52∙51∙50
132,600 ways

114. 13. In how many ways can the letters of the word MONDAY be arranged using all 6 letters?6!
6∙5∙4∙3∙2∙1
720

115. 15. Find the number of ways the letters of the word ADDEND can be arranged.
6! 3!
6∙5∙4∙3∙2∙1 3∙2∙1
6∙5∙4
120

116. 17. Find the number of ways the letters of the word ROTOR can be arranged.
5! 2!2!
5∙4∙3∙2∙1 2∙1∙2∙1 30

117. 19. Find the number of ways the letters of the word MISSISSIPPI can be arranged.
11! 4!4!2!
11∙10∙9∙8∙7∙6∙5∙4∙3∙2∙1 4∙3∙2∙1 4∙3∙2∙1 2∙1
34,650

118. 21. How many different signals can be made by displaying five flags all at one time on a flagpole? The flags differ only in color: two are red, two are white, and one is blue.
5! 2!2!1!
5∙4∙3∙2∙1 2∙1 2∙1 1 30

119. Combinations
Page 740, 1-15 all

120. 1a. For the 2-letter set {J, K}, find all the subsets
𝐽,𝐾 𝐽 𝐾 ∅

121. 1b. For the 2-letter set {J, K}, find the subsets containing fewer than 2 letters.𝐽
{𝐾} ∅

122. 2a. For the 4-digit set {1, 3, 5, 7}, find the 3-digit subsets.
1, 3, 7
1, 5, 7
{3, 5, 7}

123. 2b. For the 4-digit set {1, 3, 5, 7}, find the subsets in which the sum of the digits is at least 9.
3, 7
5, 7
1, 3, 5
1, 3, 7
1, 5, 7
3, 5, 7
{1, 3, 5, 7}

124. 3. Evaluate 5C3
5! 5−3 !3!
5∙4∙3∙2∙1 2∙1 3∙2∙1 10

125. 4. Evaluate 6C1
6! 6−1 !1!
6∙5∙4∙3∙2∙1 5∙4∙3∙2∙1 6

126. 5. Evaluate 8C6
8! 8−6 !6!
8∙7∙6∙5∙4∙3∙2∙1 (2∙1)(6∙5∙4∙3∙2∙1) 28

127. 6. Evaluate 7C4
7! 7−4 !4!
7∙6∙5∙4∙3∙2∙1 (3∙2∙1)(4∙3∙2∙1) 35

128. 7. Evaluate 10C8
10! 10−8 !8!
10∙9∙8∙7∙6∙5∙4∙3∙2∙1 2∙1 (8∙7∙6∙5∙4∙3∙2∙1) 45

129. 8. Evaluate 9C2
9! 9−2 !2!
9∙8∙7∙6∙5∙4∙3∙2∙1 (2∙1)(7∙6∙5∙4∙3∙2∙1) 36

130. 9. Evaluate 12C5
12! 12−5 !5!
12∙11∙10∙9∙8∙7∙6∙5∙4∙3∙2∙1 7∙6∙5∙4∙3∙2∙1 5∙4∙3∙2∙1
792

131. 10. Evaluate 100C2
100! 100−2 !2!
100∙99∙98∙…1 98∙97∙…1 (2)
4,950

132. 11a. How many combinations can be form the letters in EIGHT, taking them 4 at a time?
5! 5−4 !4!
5∙4∙3∙2∙1 1∙4∙3∙2∙1 5

133. 11b. How many combinations can be form the letters in EIGHT, taking them 3 at a time?
5! 5−3 !3!
5∙4∙3∙2∙1 2∙1∙3∙2∙1 10

134. 11c. How many combinations can be form the letters in EIGHT, taking them 2 at a time?
5! 5−2 !2!
5∙4∙3∙2∙1 3∙2∙1∙2∙1 10

135. 12a. How many combinations can be formed from the letters in HEXAGON, taking them 6 at a time?
7! 7−6 !1!
7∙6∙5∙4∙3∙2∙1 1∙1 7

136. 12b. How many combinations can be formed from the letters in HEXAGON, taking them 4 at a time?
7! 7−4 !4!
7∙6∙5∙4∙3∙2∙1 3∙2∙1∙4∙3∙2∙1 35

137. 12c. How many combinations can be formed from the letters in HEXAGON, taking them 2 at a time?
7! 7−2 !2!
7∙6∙5∙4∙3∙2∙1 5∙4∙3∙2∙1∙2∙1 21

138. 13. A volleyball team has 12 members, one coach, and 2 managers
13. A volleyball team has 12 members, one coach, and 2 managers. How many different combinations of 7 people can be chosen to kneel in the front row of team picture?
15C7
15! 15−7 ! 7!
15∙14∙13∙12∙11∙10∙9∙8∙7∙6∙5∙4∙3∙2∙1 8∙7∙6∙5∙4∙3∙2∙1 7∙6∙5∙4∙3∙2∙1
6,435

139. 14. A sample of 4 mousetraps taken from a batch of 100 mousetraps is to be inspected. How many different samples could be selected?
100C4
100! 100−4 !4!
100∙99∙98∙97∙96…2∙1 (96∙95∙…2∙1)(4∙3∙2∙1)
100∙99∙98∙97 4∙3∙2∙1
3,921,225

140. 15. In a group of 10 people, each person shakes hands with everyone else once. How any handshakes are there?
10C2
10! 10−2 !2!
10∙9∙8∙7∙6∙5∙4∙3∙2∙1 (8∙7∙6∙5∙4∙3∙2∙1)(2∙1) 45

141. 16. You order a hamburger with cheese, onion, pickle, relish, mustard, lettuce, tomato, or mayonnaise. How many different combinations of the “extras” can you order, choosing any four of them?
8C4
8! 8−4 !4!
8∙7∙6∙5∙4∙3∙2∙1 (4∙3∙2∙1)(4∙3∙2∙1) 70

142. 15.8 – Sample Spaces and Events
Page 744, 1-6 all

143. 1. Both dice show the same number.

144. 2. The sum of the numbers showing on the two dice is 6.

145. 3. The product of the numbers showing on the two dice is 12.

146. 4. The sum of the numbers showing on the two dice is greater than 8.

147. 5. The product of the numbers showing on the two dice is less than 10.

148. 6. The number showing on the red tie is

149. Probability
HW: Page 748, 1-7

150. 1a. A box contains 10 slips of paper numbered 1-10
1a. A box contains 10 slips of paper numbered A slip of paper is drawn at random from the box and the number is noted. Find the probability that it is a 2.
Favorable Outcomes: 1
Total Outcomes: 10
Favorable Total
1 10

151. 1b. A box contains 10 slips of paper numbered 1-10
1b. A box contains 10 slips of paper numbered A slip of paper is drawn at random from the box and the number is noted. Find the probability that it is an odd number.
Favorable Outcomes: 5
Total Outcomes: 10
Favorable Total
5 10
1 2

152. 1c. A box contains 10 slips of paper numbered 1-10
1c. A box contains 10 slips of paper numbered A slip of paper is drawn at random from the box and the number is noted. Find the probability that it is less than 4.
Favorable Outcomes: 3
Total Outcomes: 10
Favorable Total
3 10

153. 1d. A box contains 10 slips of paper numbered 1-10
1d. A box contains 10 slips of paper numbered A slip of paper is drawn at random from the box and the number is noted. Find the probability that it is less than 11.
Favorable Outcomes: 10
Total Outcomes: 10
Favorable Total
10 10 1

154. 1e. A box contains 10 slips of paper numbered 1-10
1e. A box contains 10 slips of paper numbered A slip of paper is drawn at random from the box and the number is noted. Find the probability that it is greater than 8.
Favorable Outcomes: 2
Total Outcomes: 10
Favorable Total
2 10
1 5

155. 1f. A box contains 10 slips of paper numbered 1-10
1f. A box contains 10 slips of paper numbered A slip of paper is drawn at random from the box and the number is noted. Find the probability that it is between 3 and 4.
Favorable Outcomes: 0
Total Outcomes: 10
Favorable Total
0 10

156. 2a. A letter is selected at random from those in the word TRIANGLE
2a. A letter is selected at random from those in the word TRIANGLE. Find the probability that it is a vowel.
Favorable Outcomes: 3
Total Outcomes: 8
Favorable Total
3 8

157. 2b. A letter is selected at random from those in the word TRIANGLE
2b. A letter is selected at random from those in the word TRIANGLE. Find the probability that it is a consonant.
Favorable Outcomes: 5
Total Outcomes: 8
Favorable Total
5 8

158. 2c. A letter is selected at random from those in the word TRIANGLE
2c. A letter is selected at random from those in the word TRIANGLE. Find the probability that it is from the first half of the alphabet.
First Half of the alphabet: A-M
Favorable Outcomes: 5
Total Outcomes: 8
Favorable Total
5 8

159. 2d. A letter is selected at random from those in the word TRIANGLE
2d. A letter is selected at random from those in the word TRIANGLE. Find the probability that it is between F and Q in the alphabet.
Favorable Outcomes: 4
Total Outcomes: 8
Favorable Total
4 8
1 2

160. 3a. One marble is drawn at random from a bag containing 4 white, 6 red, and 6 green marbles. Find the probability that it is white.
Favorable Outcomes: 4
Total Outcomes: 16
Favorable Total
4 16
1 4

161. 3b. One marble is drawn at random from a bag containing 4 white, 6 red, and 6 green marbles. Find the probability that it is white, red, or green.
Favorable Outcomes: 16
Total Outcomes: 16
Favorable Total
16 16 1

162. 3c. One marble is drawn at random from a bag containing 4 white, 6 red, and 6 green marbles. Find the probability that it is red or green.
Favorable Outcomes: 12
Total Outcomes: 16
Favorable Total
12 16
3 4

163. 3d. One marble is drawn at random from a bag containing 4 white, 6 red, and 6 green marbles. Find the probability that it is not red.
Favorable Outcomes: 10
Total Outcomes: 16
Favorable Total
10 16
5 8

164. 4a. One card is drawn at random from a 52-card deck
4a. One card is drawn at random from a 52-card deck. Find the probability that is an ace.
Favorable Outcomes: 4
Total Outcomes: 52
Favorable Total
4 52
1 13

165. 4b. One card is drawn at random from a 52-card deck
4b. One card is drawn at random from a 52-card deck. Find the probability that is a diamond.
Favorable Outcomes: 13
Total Outcomes: 52
Favorable Total
13 52
1 4

166. 4c. One card is drawn at random from a 52-card deck
4c. One card is drawn at random from a 52-card deck. Find the probability that is black.
Favorable Outcomes: 26
Total Outcomes: 52
Favorable Total
26 52
1 2

167. 4d. One card is drawn at random from a 52-card deck
4d. One card is drawn at random from a 52-card deck. Find the probability that it is the king of clubs.
Favorable Outcomes: 1
Total Outcomes: 52
Favorable Total
1 52

168. 4e. One card is drawn at random from a 52-card deck
4e. One card is drawn at random from a 52-card deck. Find the probability that it is a red queen.
Favorable Outcomes: 2
Total Outcomes: 52
Favorable Total
2 52
1 26

169. 4f. One card is drawn at random from a 52-card deck
4f. One card is drawn at random from a 52-card deck. Find the probability that it is a black heart.
Favorable Outcomes: 0
Total Outcomes: 52
Favorable Total
0 52

170. 5a. Two coins are tossed. Find the probability that both come up tails.
Favorable Outcomes: 1
Total Outcomes: 4
Favorable Total
1 4
TT TH
HT HH

171. 5b. Two coins are tossed. Find the probability that at least one coin comes up heads.
Favorable Outcomes: 3
Total Outcomes: 4
Favorable Total
3 4
TT TH
HT HH

172. 5c. Two coins are tossed. Find the probability that the coins match.
Favorable Outcomes: 2
Total Outcomes: 4
Favorable Total
2 4
1 2
TT TH
HT HH

173. 5d. Two coins are tossed. Find the probability that coins don’t match.
Favorable Outcomes: 2
Total Outcomes: 4
Favorable Total
2 4
1 2
TT TH
HT HH

174. 6a. A 10-speed bicycle is given as a door prize
6a. A 10-speed bicycle is given as a door prize. A total of 220 tickets numbered are sold. If the winning number is chosen at random, find the probability that the winning number is less than 101.
Favorable Outcomes: 100
Total Outcomes: 220
Favorable Total
5 11

175. 6b. A 10-speed bicycle is given as a door prize
6b. A 10-speed bicycle is given as a door prize. A total of 220 tickets numbered are sold. If the winning number is chosen at random, find the probability that the winning number is greater than 50.
Favorable Outcomes: 170
Total Outcomes: 220
Favorable Total
17 22

176. 6c. A 10-speed bicycle is given as a door prize
6c. A 10-speed bicycle is given as a door prize. A total of 220 tickets numbered are sold. If the winning number is chosen at random, find the probability that the winning number is between 10 and 21.
Favorable Outcomes: 10
Total Outcomes: 220
Favorable Total
10 220
1 22

177. 7a. Of 1,000,000 income tax returns received, all are checked for arithmetic accuracy and 9,000 returns, selected at random, are checked thoroughly. For a given return, find the probability that it is checked for arithmetic accuracy.
Favorable Outcomes: 100,000,000
Total Outcomes: 1,000,000
Favorable Total
1,000,000 1,000,000 1

178. 7b. Of 1,000,000 income tax returns received, all are checked for arithmetic accuracy and 9,000 returns, selected at random, are checked thoroughly. For a given return, find the probability that it is checked thoroughly.
Favorable Outcomes: 9,000
Total Outcomes: 1,000,000
Favorable Total
9,000 1,000,000
9 1000

179. 7c. Of 1,000,000 income tax returns received, all are checked for arithmetic accuracy and 9,000 returns, selected at random, are checked thoroughly. For a given return, find the probability that it is not checked thoroughly.
Favorable Outcomes: 991,000
Total Outcomes: 1,000,000
Favorable Total
991,000 1,000,000

180. 8a. Two dice are rolled. Find the probability that the sum of the numbers showing on the dice is 10.
2, 1
2, 2
2, 3
2, 4
2, 5
2, 6
3, 1
3, 2
3, 3
3, 4
3, 5
3, 6
4, 1
4, 2
4, 3
4, 4
4, 5
4, 6
6, 1
6, 2
6, 3
6, 4
6, 5
6, 6
1, 1
1, 2
1, 3
1, 4
1, 5
1, 6
5, 1
5, 2
5, 3
5, 4
5, 5
5, 6
Favorable Outcomes: 3
Total Outcomes: 36
Favorable Total
1 12 1

181. 8b. Two dice are rolled. Find the probability that the sum is at least 10.
2, 1
2, 2
2, 3
2, 4
2, 5
2, 6
3, 1
3, 2
3, 3
3, 4
3, 5
3, 6
4, 1
4, 2
4, 3
4, 4
4, 5
4, 6
6, 1
6, 2
6, 3
6, 4
6, 5
6, 6
1, 1
1, 2
1, 3
1, 4
1, 5
1, 6
5, 1
5, 2
5, 3
5, 4
5, 5
5, 6
Favorable Outcomes: 6
Total Outcomes: 36
Favorable Total
6 36
1 6

182. 8c. Two dice are rolled. Find the probability that exactly one die shows a 4.
2, 1
2, 2
2, 3
2, 4
2, 5
2, 6
3, 1
3, 2
3, 3
3, 4
3, 5
3, 6
4, 1
4, 2
4, 3
4, 4
4, 5
4, 6
6, 1
6, 2
6, 3
6, 4
6, 5
6, 6
1, 1
1, 2
1, 3
1, 4
1, 5
1, 6
5, 1
5, 2
5, 3
5, 4
5, 5
5, 6
Favorable Outcomes: 3
Total Outcomes: 36
Favorable Total
1 12 1

183. 8d. Two dice are rolled. Find the probability that at least one die shows a 4.
2, 1
2, 2
2, 3
2, 4
2, 5
2, 6
3, 1
3, 2
3, 3
3, 4
3, 5
3, 6
4, 1
4, 2
4, 3
4, 4
4, 5
4, 6
6, 1
6, 2
6, 3
6, 4
6, 5
6, 6
1, 1
1, 2
1, 3
1, 4
1, 5
1, 6
5, 1
5, 2
5, 3
5, 4
5, 5
5, 6
Favorable Outcomes: 11
Total Outcomes: 36
Favorable Total
11 36

184. 15.10 – Mutually Exclusive and Independent Events
HW: Page 759, 1-9 all

185. 1a. Tanya randomly guesses a whole number from 1 to 10
1a. Tanya randomly guesses a whole number from 1 to 10. Find the probability that she guesses a number less than 6.
Favorable: 5
Total: 10
𝐹𝑎𝑣𝑜𝑟𝑎𝑏𝑙𝑒 𝑇𝑜𝑡𝑎𝑙
5 10
1 2

186. 1b. Tanya randomly guesses a whole number from 1 to 10
1b. Tanya randomly guesses a whole number from 1 to 10. Find the probability that she guesses an odd number.
Favorable: 5
Total: 10
𝐹𝑎𝑣𝑜𝑟𝑎𝑏𝑙𝑒 𝑇𝑜𝑡𝑎𝑙
5 10
1 2

187. 1c. Tanya randomly guesses a whole number from 1 to 10
1c. Tanya randomly guesses a whole number from 1 to 10. Find the probability that she guesses an odd number less than 6.
Favorable: 3
Total: 10
𝐹𝑎𝑣𝑜𝑟𝑎𝑏𝑙𝑒 𝑇𝑜𝑡𝑎𝑙
3 10

188. 2a. A single marble is drawn from a bag containing 3 red, 5 white, and 2 blue marbles. Find the probability that a red or blue marble is drawn.
Favorable: 5
Total: 10
𝐹𝑎𝑣𝑜𝑟𝑎𝑏𝑙𝑒 𝑇𝑜𝑡𝑎𝑙
5 10
1 2

189. 2b. A single marble is drawn from a bag containing 3 red, 5 white, and 2 blue marbles. Find the probability that a blue or white marble is drawn.
Favorable: 7
Total: 10
𝐹𝑎𝑣𝑜𝑟𝑎𝑏𝑙𝑒 𝑇𝑜𝑡𝑎𝑙
7 10

190. 2c. A single marble is drawn from a bag containing 3 red, 5 white, and 2 blue marbles. Find the probability that a red, white, or blue marble is drawn.
Favorable: 10
Total: 10
𝐹𝑎𝑣𝑜𝑟𝑎𝑏𝑙𝑒 𝑇𝑜𝑡𝑎𝑙
10 10 1

191. 3a. The names of 3 seniors, 4 juniors, and 5 sophomores are placed in a bowl. One name is drawn at random, set aside, and a second name is then drawn at random. Find the probability that the first name draw in a junior and the second is a senior.
Probability of Event 1:
Probability of Event 2:
Probability of both Events: ∙ 3 11
Probability of both Events:

192. 3b. The names of 3 seniors, 4 juniors, and 5 sophomores are placed in a bowl. One name is drawn a t random, set aside, and a second name is then drawn at random. Find the probability that both names drawn are sophomores.
Probability of Event 1:
Probability of Event 2:
Probability of both Events: ∙ 4 11
Probability of both Events:

193. 4a. There are 3 red, 2 blue, and 3 yellow crayons in a box
4a. There are 3 red, 2 blue, and 3 yellow crayons in a box. Jeff randomly selects one, returns it to the box, and then randomly selects another. Find the probability that the first crayon selected is blue and the second is yellow.
Probability of Event 1: 2 8
Probability of Event 2: 3 8
Probability of both Events: ∙ 3 8
Probability of both Events:

194. 4b. There are 3 red, 2 blue, and 3 yellow crayons in a box
4b. There are 3 red, 2 blue, and 3 yellow crayons in a box. Jeff randomly selects one, returns it to the box, and then randomly selects another. Find the probability that both crayons selected are red.
Probability of Event 1: 3 8
Probability of Event 2: 3 8
Probability of both Events: ∙ 3 8
Probability of both Events:

195. 5a. A red and a green die are rolled
5a. A red and a green die are rolled. Let A be the event that the red die shows 2 and B be the event that the sum of the numbers showing is 8. Find the probability of A, B, 𝐴∪𝐵, and 𝐴∩𝐵.
2, 1
2, 2
2, 3
2, 4
2, 5
2, 6
3, 1
3, 2
3, 3
3, 4
3, 5
3, 6
4, 1
4, 2
4, 3
4, 4
4, 5
4, 6
6, 1
6, 2
6, 3
6, 4
6, 5
6, 6
1, 1
1, 2
1, 3
1, 4
1, 5
1, 6
5, 1
5, 2
5, 3
5, 4
5, 5
5, 6
Probability of A = 1 6
Probability of B = 5 36
Probability of 𝐴∪𝐵 = = 5 18
Probability of 𝐴∩𝐵 = 1 36

196. 5b. A red and a green die are rolled
5b. A red and a green die are rolled. Let A be the event that the red die shows 2 and B be the event that the sum of the numbers showing is 8. Are A and B independent events? No

197. 6a. A die and a coin are tossed
6a. A die and a coin are tossed. Let A be the event that the die shows a 5 or 6, and let B be the event that the coin shows heads. Specify the sample space for the experiment.
1,𝐻 , 2,𝐻 , 3,𝐻 , 4,𝐻 , 5,𝐻 , 6,𝐻 , 1,𝑇 , 2,𝑇 , 3,𝑇 , 4,𝑇 , 5,𝑇 , 6,𝑇

198. 6b. A die and a coin are tossed
6b. A die and a coin are tossed. Let A be the event that the die shows a 5 or 6, and let B be the event that the coin shows heads. Specify the simple events in A, B, 𝐴∪𝐵, 𝐴∩𝐵.
A: 5,𝐻 , 6,𝐻 , 5,𝑇 , 6,𝑇 B: 1,𝐻 , 2,𝐻 , 3,𝐻 , 4,𝐻 , 5,𝐻 , 6,𝐻 𝐴∪𝐵: 5,𝐻 , 6,𝐻 , 5,𝑇 , 6,𝑇 , 1,𝐻 , 2,𝐻 , 3,𝐻 , 4,𝐻 𝐴∩𝐵: 5,𝐻 , 6,𝐻

199. 6c. A die and a coin are tossed
6c. A die and a coin are tossed. Let A be the event that the die shows a 5 or 6, and let B be the event that the coin shows heads. Find the probability of A, B, 𝐴∪𝐵, and 𝐴∩𝐵.
A: 4 12 = 1 3 B: 6 12 = 1 2 𝐴∪𝐵: 8 12 = 2 3 𝐴∩𝐵: 2 12 = 1 6

200. 6d. A die and a coin are tossed
6d. A die and a coin are tossed. Let A be the event that the die shows a 5 or 6, and let B be the event that the coin shows heads. Are A and B mutually exclusive? Are they independent?
No Yes

201. 7a. Two dice are rolled. Find the probability that the sum of the numbers showing is 10.
2, 1
2, 2
2, 3
2, 4
2, 5
2, 6
3, 1
3, 2
3, 3
3, 4
3, 5
3, 6
4, 1
4, 2
4, 3
4, 4
4, 5
4, 6
6, 1
6, 2
6, 3
6, 4
6, 5
6, 6
1, 1
1, 2
1, 3
1, 4
1, 5
1, 6
5, 1
5, 2
5, 3
5, 4
5, 5
5, 6

202. 7b. Two dice are rolled. Find the probability that either the sum of the numbers showing is 4 or both numbers are 4.
2, 1
2, 2
2, 3
2, 4
2, 5
2, 6
3, 1
3, 2
3, 3
3, 4
3, 5
3, 6
4, 1
4, 2
4, 3
4, 4
4, 5
4, 6
6, 1
6, 2
6, 3
6, 4
6, 5
6, 6
1, 1
1, 2
1, 3
1, 4
1, 5
1, 6
5, 1
5, 2
5, 3
5, 4
5, 5
5, 6

203. 8a. Two cards are drawn at the same time from a 52-card deck
8a. Two cards are drawn at the same time from a 52-card deck. Find the probability that both cards are jacks.
1st card is a Jack: nd card is a Jack: ∙

204. 8b. Two cards are drawn at the same time from a 52-card deck
8b. Two cards are drawn at the same time from a 52-card deck. Find the probability that both cards are sixes.
1st card is a 6: nd card is a 6: ∙

205. 8c. Two cards are drawn at the same time from a 52-card deck
8c. Two cards are drawn at the same time from a 52-card deck. Find the probability that either both cards are jacks or both are sixes.
Both Cards are Jacks: Both Cards are sixes:

206. 9a. A coin is tossed three times
9a. A coin is tossed three times. Find the probability that at least two tosses come up tails.
TTH
THT
HTT
HHT
HTH
THH
HHH
TTT

207. 9b. A coin is tossed three times
9b. A coin is tossed three times. Find the probability that at least one toss comes up heads.
7 8
TTH
THT
HTT
HHT
HTH
THH
HHH
TTT

208. 10a. From a 52-card deck a card is drawn and then replaced
10a. From a 52-card deck a card is drawn and then replaced. After the deck is shuffled, a second card is drawn. Find the probability that the first card is a 5 and the second is a 6.
Probability of a 5: 4 52 = 1 13 Probability of a 6: 4 52 = 1 13 Probability of both: 1 13 ∙ 1 13 Probability of both: 1 169

209. 10b. From a 52-card deck a card is drawn and then replaced
10b. From a 52-card deck a card is drawn and then replaced. After the deck is shuffled, a second card is drawn. Find the probability that both cards are clubs.
Probability of a club: 1 4 Probability of both: 1 4 ∙ 1 4 = 1 16