1. Dates of … Quiz 5.4 – 5.5 Chapter 5 homework quiz Chapter 5 test
Both sides of one note card
2nd Quarter project work day

2. Sections 5.4 – 5.5

3. Two events are disjoint if __________.

4. Two events are disjoint if they can not happen on the same opportunity.

5. If A and B are disjoint events, then
P(A and B) is _____.

6. If A and B are disjoint events, then
P(A and B) is 0.

7. Two events are independent if __________.

8. Two events are independent if the occurrence of one event does not change the probability that the other event will happen.

9. Two events are independent if the occurrence of one event does not change the probability that the other event will happen.
Two events are independent if and only if P(A) = P(A B).

10. Two events are independent if and only if P(A) = P(A B).
P(A and B) = P(A) ● P(B), where P(A) > 0 and P(B) > 0.

11. What is the Addition Rule for any two events A and B?

12. P(A or B) = P(A) + P(B) – P(A and B)
What is the Addition Rule for any two events A and B?
P(A or B) = P(A) + P(B) – P(A and B)

13. What is the Multiplication Rule?

14. Multiplication Rule
The probability that event A and event B both happen is given by:
P(A and B) = P(A)●P(B A) or
P(A and B) = P(B)●P(A B)

15. Multiplication Rule for Independent Events
P(A and B) = P(A) ● P(B), where
P(A) > 0 and P(B) > 0.

16. P(at least one success) = ?

17. P(at least one success) =
1 – P(no successes)

18. Complete this table so that the events survived and male are independent. Show your work.
Male Female Total
Survived
650
Did Not Survive
Total
1640
2000

19. Complete this table so that the events survived and male are independent. Show your work.
Male Female Total
Survived
650
Did Not Survive
1350
Total
1640
360
2000

20. Complete this table so that the events survived and male are independent. Show your work.
Male Female Total
Survived
650
Did Not Survive
1350
Total
1640
360
2000
P(A) = P(A I B)

21. Complete this table so that the events survived and male are independent. Show your work.
Male Female Total
Survived
650
Did Not Survive
1350
Total
1640
360
2000
P(A) = P(A I B)
P(Survived) = P(Survived I Male)

22. Complete this table so that the events survived and male are independent. Show your work.
Male Female Total
Survived
650
Did Not Survive
1350
Total
1640
360
2000

23. Complete this table so that the events survived and male are independent. Show your work.
Male Female Total
Survived x
650
Did Not Survive
1350
Total
1640
360
2000

24. Complete this table so that the events survived and male are independent. Show your work.
Male Female Total
Survived
533
650
Did Not Survive
1350
Total
1640
360
2000

25. Complete this table so that the events survived and male are independent. Show your work.
Male Female Total
Survived
533
117
650
Did Not Survive
1107
243
1350
Total
1640
360
2000

26. Page 335, P32

27. Page 335, P32 Right-Handed Left-Handed Total Blue Eyes
_______________________________
Brown Eyes
Total

28. Page 335, P32 Right-Handed Left-Handed Total Blue Eyes 2 10
_______________________________
Brown Eyes
Total

29. Page 335, P32
P(Right-handed I Brown eyes) = ?

30. Page 335, P32

31. Page 335, P32
Are the events right-handed and brown eyes independent?

32. Page 335, P32
Are the events right-handed and brown eyes independent? P(A) = P(A B)?
Is P(right-handed) = P(right-handed brown eyes)?

33. Page 335, P32 P(right-handed) = 24/30 = 0.8
P(right-handed brown eyes) = 16/20 = 0.8
these are independent events.

34. Page 335, P32
Are the events right-handed and brown eyes independent? P(B) = P(B A)?

35. Page 335, P32 Are the events right-handed and brown eyes independent?
Is P(brown eyes) = P(brown eyes right-handed)?

36. Page 335, P32 P(brown eyes) = 20/30 = 2/3
P(brown eyes right-handed) = 16/24 = 2/3
these are independent events.

37. Page 346, E59

38. Page 346, E59

39. Page 346, E59

40. Page 346, E59

41. Page 346, E59

42. Page 346, E59

43. Page 346, E59

44. Page 347, E63

45. Page 347, E63
a. P(Type O blood and Rh-positive) =

46. Page 347, E63

47. Page 347, E63
b. P(Type O blood or Rh-positive) =

48. Page 347, E63 b. P(Type O blood or Rh-positive) =
Are these disjoint events?

49. Page 347, E63 b. P(Type O blood or Rh-positive) =
Are these disjoint events? No
So need to avoid double-counting outcomes.

50. Page 347, E63

51. Page 347, E63
c. Make a table that summarizes this situation.

52. Page 347, E63
c Rh-positive
Yes No Total
Yes
Type O No
Total

53. Page 347, E63 c. Rh-positive Yes No Total Yes 2.1 42 Type O No

54. Page 347, E63

55. Review Continued

56. Page 338, E51

57. Positive Negative Total
Page 338, E51
Test Result
Positive Negative Total
Yes
Disease No
Total ,000

58. Disease occurs in about 3% of population.
Page 338, E51
Disease occurs in about 3% of population.
Test Result
Positive Negative Total
Yes
Disease No
Total ,000

59. Disease occurs in about 3% of population.
Page 338, E51
Disease occurs in about 3% of population.
Test Result
Positive Negative Total
Yes ,000
Disease No
Total ,000

60. Positive Negative Total
Page 338, E51
Test Result
Positive Negative Total
Yes ,000
Disease
No ,000
Total ,000

61. Positive result 6% of time for people without the disease.
Page 338, E51
Positive result 6% of time for people without the disease.
Test Result
Positive Negative Total
Yes ,000
Disease
No ,000
Total ,000

62. Positive result 6% of time for people without the disease.
Page 338, E51
Positive result 6% of time for people without the disease.
Test Result
Positive Negative Total
Yes ,000
Disease
No 6%(97000) = ,000
5820
Total ,000

63. Positive Negative Total
Page 338, E51
Test Result
Positive Negative Total
Yes ,000
Disease
No ,000
Total ,000

64. Positive Negative Total
Page 338, E51
Negative result 0.5% of time for people with the disease
Test Result
Positive Negative Total
Yes ,000
Disease
No ,000
Total ,000

65. Positive Negative Total
Page 338, E51
Negative result 0.5% of time for people with the disease
Test Result
Positive Negative Total
Yes 0.5%(3000) ,000
Disease = 15
No ,000
Total ,000

66. Positive Negative Total
Page 338, E51
Test Result
Positive Negative Total
Yes ,000
Disease
No ,000
Total ,000

67. Positive Negative Total
Page 338, E51
Test Result
Positive Negative Total
Yes ,000
Disease
No ,000
Total ,000

68. Positive Negative Total
Page 338, E51(b) ≈ 0.088
Test Result
Positive Negative Total
Yes ,000
Disease
No ,000
Total ,000

69. Positive Negative Total
Page 338, E51(c) ≈ 0.661
Test Result
Positive Negative Total
Yes ,000
Disease
No ,000
Total ,000

70. You are going to draw two cards from a standard deck of cards
You are going to draw two cards from a standard deck of cards. What must happen to ensure pairs of successive selections are independent?

71. You are going to draw two cards from a standard deck of cards
You are going to draw two cards from a standard deck of cards. What must happen to ensure pairs of successive selections are independent?
The first card must be replaced in the deck before the second card is drawn.

72. Suppose you roll a fair die and get a 3 seven times in a row
Suppose you roll a fair die and get a 3 seven times in a row. What is the probability you will get a 3 on the next roll?

73. Suppose you roll a fair die and get a 3 seven times in a row
Suppose you roll a fair die and get a 3 seven times in a row. What is the probability you will get a 3 on the next roll?
The die has no memory so each roll is an independent event.
P(3 on next roll) = 1/6

74. The proportion of 18-year-olds who are registered to vote is approximately 15%.
Describe how to use the following lines from a random digit table to simulate taking a sample of ten 18-year-olds and recording whether they are registered to vote.

75. Model Registered to vote: 01 - 15 Not registered to vote: 16 – 99, 00or
Registered to vote:
Not registered to vote: 15 – 99

76. b. Start at the beginning of the first line, take three samples of size 10, and compute the sample proportion for each sample. (Do not start a new line for each sample. Start where the previous sample finished.)

77. b. Start at the beginning of the first line, take three samples of size 10, and compute the sample proportion for each sample. (Do not start a new line for each sample. Start where the previous sample finished.)
Sample 1
EduBallot online voting instructions

78. b. Start at the beginning of the first line, take three samples of size 10, and compute the sample proportion for each sample. (Do not start a new line for each sample. Start where the previous sample finished.)
Sample 1
EduBallot online voting instructions

79. b. Start at the beginning of the first line, take three samples of size 10, and compute the sample proportion for each sample. (Do not start a new line for each sample. Start where the previous sample finished.)
Sample 1
Sample 2
EduBallot online voting instructions

80. b. Start at the beginning of the first line, take three samples of size 10, and compute the sample proportion for each sample. (Do not start a new line for each sample. Start where the previous sample finished.)
Sample 1
Sample 2
EduBallot online voting instructions

81. b. Start at the beginning of the first line, take three samples of size 10, and compute the sample proportion for each sample. (Do not start a new line for each sample. Start where the previous sample finished.)
Sample 1
Sample 2
Sample 3
EduBallot online voting instructions

82. b. Start at the beginning of the first line, take three samples of size 10, and compute the sample proportion for each sample. (Do not start a new line for each sample. Start where the previous sample finished.)
Sample 1
Sample 2
Sample 3
EduBallot online voting instructions

83. b. Sample 1: Using the assignment 01–15 for registered 18-year-olds, you’ll find the sample proportion is 2/10 or 0.2. Using the assignment 00–14 for registered 18-year-olds, you’ll find the sample proportion is 1/10 or 0.1.
Sample 2: Using either assignment from part a, you’ll find the sample proportion is 0/10 or 0.
Sample 3: Using either assignment from part a, you’ll find the sample proportion is 0/10, or 0.

84. Questions?