chapter 4 (and questions on paper)

68. If A and B are independent events with P(A) = .4 and P(B) = .25, then P(A ∪ B) = _____.

.55

45. If P(A) = .75, P(A ∪ B) = .86, and P(A ∩ B) = .56, then P(B) =

.67

67. If A and B are independent events with P(A) = .2 and P(B) = .6, then P(A ∪ B) = _____.

.68

58. If P(A) = .62, P(B) = .56, and P(A ∪ B) = .70, then P(B | A) = _____.

.7742

32. A professor rolls a fair, six-sided die. Using the classical method of probability, what is the probability that at least three spots will be showing up on the die?

2/3

26. The "Top Three" at a racetrack consists of picking the correct order of the first three horses in a race. If there are 10 horses in a particular race, how many "Top Three" outcomes are there?

720

3. Posterior probabilities are computed using _____.

Bayes' theorem

40. The probability of the union of two events with nonzero probabilities _____.

None of the answers are correct (below) -cannot be less than 1 -cannot be 1 -cannot be less than one and cannot be 1

4. The complement of P(A | B) is _____.

P(A^c | B)

39. The union of events A and B is the event containing _____.

all the sample points belonging to A or B or both

11. Any process that generates well-defined outcomes is _____.

an experiment

62. Two events with nonzero probabilities _____.

cannot be both mutually exclusive and independent

63. If P(A) = .50, P(B) = .60, and P(A ∩ B) = .30, then events A and B are _____.

independent events

36. A(n) __________ is a collection of sample points.

event

55. One of the basic requirements of probability is _____.

if there are k experimental outcomes, then P(E1) + P(E2) + ... + P(Ek) = 1

29. When the results of experimentation or historical data are used to assign probability values, the method used to assign probabilities is referred to as the _____.

relative frequency method

57. The multiplication law is potentially helpful when we are interested in computing the probability of _____.

the intersection of two events

77. Bayes' theorem is used to compute _____.

the posterior probabilities

15. The collection of all possible sample points in an experiment is _____.

the sample space

17. The sample space refers to _____.

the set of all possible experimental outcomes

37. Given that event E has a probability of .25, the probability of the complement of event E _____.

must be .75

30. A method of assigning probabilities based upon judgment is referred to as the _____.

None of the answers are correct (below) -relative frequency method -probability method -classical method

85. If P(A | B) = .3 and P(B) = .8, then _____.

P(A ∩ B) = .24

54. Which of the following statements is always true?

P(A) = 1 − P(A^c)

83. If P(A | B) = 0.3,

P(A^c | B) = 0.7

24. A graphical device used for enumerating sample points in a multiple-step experiment is a _____.

tree diagram

34. A graphical method of representing the sample points of a multiple-step experiment is a(n) _____.

tree diagram

49. If two events are mutually exclusive, then the probability of their intersection _____.

will be equal to 0

1. The probability of at least one head in two flips of a coin is _____.

75

81. If P(A ∩ B) = 0, _____.

A and B are mutually exclusive events

44. If P(A) = .62, P(B) = .47, and P(A ∪ B) = .88; then P(A ∩ B) =

.210

43. If P(A) = .38, P(B) = .83, and P(A ∩ B) = .24; then P(A ∪ B) =

.97

92. A committee of four is to be selected from a group of 12 people. How many possible committees can be selected?

495

69. Events A and B are mutually exclusive. Which of the following statements is also true?

P(A ∪ B) = P(A) + P(B)

70. If A and B are independent events with P(A) = .05 and P(B) = .65, then P(A | B) = _____.

.05

19. An experiment consists of tossing four coins successively. The number of sample points in this experiment is _____.

16

23. Each customer entering a department store will either buy or not buy some merchandise. An experiment consists of following three customers and determining whether or not they purchase any merchandise. The number of sample points in this experiment is _____.

8

16. Twenty percent of people at a company picnic got food poisoning. What percent of the people at the picnic did NOT get food poisoning?

80%

7. If A and B are mutually exclusive, then _____.

P(A ((square)) B) = 0

84. If A and B are independent events with P(A) = 0.1 and P(B) = .4, then _____.

P(A ∩ B) = .04

35. A __________ is a graphical representation in which the sample space is represented by a rectangle and events are represented as circles.

Venn diagram

46. Two events are mutually exclusive if _____.

they have no sample points in common

64. On a December day, the probability of snow is .30. The probability of a "cold" day is .50. The probability of snow and a "cold" day is .15. Are snow and "cold" weather independent events?

yes

86. If P(A) = .6, P(B) = .3, and P(A ∩ B) = .2, then P(B | A) =_____.

.33

87. If P(A) = .85, P(B) = .76, and P(A ∩ B) = .72, then P(A | B) = _____.

.95

9. The range of probability is _____,

0 to 1, inclusive

71. A six-sided die is rolled three times. The probability of observing a 1 three times in a row is _____.

1/216

21. Three applications for admission to a local university are checked to determine whether each applicant is male or female. The number of sample points in this experiment is _____.

8

22. Assume your favorite football team has two games left to finish the season. The outcome of each game can be win, lose, or tie. The number of possible outcomes is _____.

9

8. Posterior probabilities are _____.

conditional probabilities

42. The addition law is potentially helpful when we are interested in computing the probability of _____.

the union of two events

53. In an experiment, events A and B are mutually exclusive. If P(A) = .6, then the probability of B _____.

cannot be larger than .4

6. The probability of an intersection of two events is computed using the _____.

multiplication law

10. Since the sun MUST rise tomorrow, then the probability of the sun rising tomorrow is _____.

None of the answers are correct (below) -much larger than 1 -0 -infinity

41. The symbol ∩ shows the _____.

intersection of events

2. Revised probabilities of events based on additional information are _____.

posterior probabilities

78. Initial estimates of the probabilities of events are known as _____.

prior probabilities

52. If A and B are mutually exclusive events with P(A) = .3 and P(B) = .5, then P(A ∪ B) =

.8

88. If P(A) = .80, P(B) = .65, and P(A ∩ B) = .78, then P(B A) = _____.

.8375

12. Suppose we flip a fair coin five times and each time it lands heads up. The probability of landing heads up on the next flip is _____.

1/2

73. If a fair penny is tossed four times and comes up heads all four times, the probability of heads on the fifth trial is _____.

1/2

18. An experiment consists of three steps. There are four possible results on the first step, three possible results on the second step, and two possible results on the third step. The total number of experimental outcomes is _____.

24

56. Events A and B are mutually exclusive with P(A) = .3 and P(B) = .2. The probability of the complement of event B equals _____.

None of the answers are correct (below) 0 .06 .70

65. If P(A) = .5 and P(B) = .5, then P(A ∩ B) _____.

cannot be determined from the information given

33. An experiment consists of four outcomes with P(E1) = .2, P(E2) = .3, and P(E3) = .4. The probability of outcome E4 is _____.

.100

66. If A and B are independent events with P(A) = .4 and P(B) = .6, then P(A ∩ B) = _____.

.24

20. A lottery is conducted using three urns. Each urn contains chips numbered from 0 to 9. One chip is selected at random from each urn. The total number of sample points in the sample space is _____.

1,000

27. When the assumption of equally likely outcomes is used to assign probability values, the method used to assign probabilities is referred to as the _____.

classical method

14. A sample point refers to a(n) _____.

individual outcome of an experiment

76. The probability of the occurrence of event A in an experiment is 1/3. If the experiment is performed two times and event A did not occur, then on the third trial event A _____.

may occur

38. The symbol ∪ indicates the _____.

union of events

31. Of the last 100 customers entering a computer shop, 25 have purchased a computer. If the relative frequency method for computing probability is used, the probability that the next customer will purchase a computer is _____.

.25

13. There is a 60% chance of getting stuck in traffic when leaving the city. On two separate days, what is the probability that you get stuck in traffic both days?

.36

75. A couple has three children. Assuming each child has an equal chance of being a boy or a girl, what is the probability that they have at least one girl?

.875

50. Two events, A and B, are mutually exclusive and each has a nonzero probability. If event A is known to occur, the probability of the occurrence of event B is _____.

0

61. If X and Y are mutually exclusive events with P(X) = .295, P(Y) = .32, then P(X ∪ Y) = _____.

0

91. A student has to take seven more courses before she can graduate. If none of the courses are prerequisites to others, how many groups of three courses can she select for the next semester?

35

5. An element of the sample space is a(n) _____.

sample point

28. A magician holds a standard deck of cards and draws one card. The probability of drawing the ace of diamonds is 1/52. What method of assigning probabilities was used?

classical method

72. If a coin is tossed three times, the likelihood of obtaining three heads in a row is _____.

.125

51. If A and B are mutually exclusive events with P(A) = .3 and P(B) = 0.5, then P(A ∩ B) =

0

25. Of five letters (A, B, C, D, and E), two letters are to be selected at random. How many possible selections are there?

10

89. All the employees of ABC Company are assigned ID numbers. The ID number consists of the first letter of an employee's last name, followed by four numbers. a.) How many possible different ID numbers are there? b.) How many possible different ID numbers are there for employees whose last name starts with an "A"?

a.) 260,000 b.) 10,000v

90. A company plans to interview 10 recent graduates for possible employment. The company has three positions open. How many groups of three can the company select?

120

74. If a fair penny is tossed three times and comes up heads all three times, the probability of heads on the fourth trial is _____.

None of the answers are correct (below) -smaller than the probability of tails -larger than the probability of tails - 1/16

59. If two events are independent, then _____.

None of the answers are correct (below) -they must be mutually exclusive -the sum of their probabilities must be equal to 1 -the probability of their intersection must be 0

60. If A and B are independent events with P(A) = .38 and P(B) = .55, then P(A | B) =

None of the answers are correct (below) .209 0 .550

48. The probability of the intersection of two mutually exclusive events _____.

must always be equal to 0

47. You roll a fair six-sided die with the hopes of rolling a 5 or a 6. These two events are ___________ because they have no sample points in common.

mutually exclusive events

82. The probability of an event is _____.

the sum of the probabilities of the sample points in the event