Econ 2300 KSU Test 3

13. A dormitory on campus houses 200 students. 120 are male, 50 are upper division students, and 40 are upper division male students. A student is selected at random. The probability of selecting a lower division student, given the student is a female, is: (a) 7/8 (b) 7/15 (c) 2/5 (d) 7/20 (e) ¼

(a) 7/8

15. Among twenty-five articles eight are defective, six having only minor defects and two having major defects. Determine the probability that an article selected at random has major defects given that it has defects. (a) .08 (b) .25 (c) 1/3 (d) .24

(b) .25

2. Two mutually exclusive events having positive probabilities are ______________ dependent. A. Always B. Sometimes C. Never

A. Always

64. Suppose a certain opthalmic trait is associated with eye color. 300 randomly selected individuals are studied with results as follows: EYE COLOR TRAIT | Blue | Brown | Other | Total ____________________________________ Yes | 70 | 30 | 20 | 120 ____________________________________ No | 20 | 110 | 50 | 180 ____________________________________ Total | 90 | 140 | 70 | 300 A. What is the probability that a person has blue eyes? B. What would you expect to be the value P(having the trait and blue eyes) if eye color and trait status were independent?

A. Ans. .3 B. Ans. .12

Which of the following is FALSE? a. Always P(A∪B)=P(B∪A) b. Always P(A∩B)=P(B∩A) c. Always P(A|B)=P(B|A) d. Always P(A complement) = 1-P(A)

Always P(A|B)=P(B|A)

1. The _____ of an event is a number that measures the likelihood that an event will occur when an experiment is carried out. A. Outcome B. Probability C. Intersection D. Observation

B Probability

6. P(AUB) = P(A) + P(B) - P(A n B) represents the formula for the A. conditional probability B. addition rule C. addition rule for two mutually exclusive events D. multiplication rule

B. addition rule

66. A survey indicates that 45.8% of customers rented a car for business reasons, 54% for personal reasons, and 30% rented for both business and personal reasons. Based on the information provided, complete the joint probability table below. Business Reasons Not Business Reasons Total Personal Reasons Not Personal Reasons Total

Business Reasons Not Business Reasons Total Personal Reasons 0.300 0.240 0.540 Not Personal Reasons 0.158 0.302 0.460 Total 0.458 0.542 1.000

3. If two events are independent, we can _____ their probabilities to determine the intersection probability. A. Divide B. Add C. Multiply D. Subtract

C Multiply

7. Suppose a certain opthalmic trait is associated with eye color. 300 randomly selected individuals are studied with results as follows: EYE COLOR TRAIT | Blue | Brown | Other | Total ____________________________________ Yes | 70 | 30 | 20 | 120 ____________________________________ No | 20 | 110 | 50 | 180 ____________________________________ Total | 90 | 140 | 70 | 300 Which of the following expressions describes the relationship between the events A = a person has brown eyes and B = a person has blue eyes? A. independent B. exhaustive C. simple D. mutually exclusive

D. mutually exclusive

4. A ____________ is the probability that one event will occur given that we know that another event already has occurred. A. Sample space outcome B. Subjective Probability C. Complement of events D. Long-run relative frequency E. Conditional probability

E. Conditional Probability

5. The _______ of two events X and Y is another event that consists of the sample space outcomes belonging to either event X or event Y or both event X and Y. A. Complement B. Union C. Intersection D. Conditional probability E. Union

E. Union

78. Coin and Die Event A = {a fair coin comes up Heads} Event B = {a fair die comes up Six} Find P(Head and 6)

Event A and B are independent P(Head and 6) = 1/2 X 1/6 = 1/12

79. Event {Flip a coin twice} Find P (Head in the first flip or in the second flip)

Flips are independent here. P (Head in the first flip) + P (Head in the second flip) - P (Head in both) = 1/2 + 1/2 - 1/4 = 3/4

A survey of 880 individuals asked for their favorite drink between beer and wine. Beer B Wine W Male M 330 140 Female F 120 290 Beer B Wine W Total Male M 330 140 470 Female F 120 290 410 Total 450 430 880

Joint Probability Table Beer B Wine W Total Male M 0.375 0.159 0.534 Female F 0.136 0.330 0.466 Total 0.511 0.489 1.000

77. Flip a coin twice. Event A = { Head on flip 1} Event B = { Head on flip 2} Find P (Head on flip 1 and Head on flip 2)

P (Head on flip 1) = 1/2 P = { Head on flip 2} = 1/2 Since events are independent, P (Head on flip 1 and Head on flip 2) = 1/2 X 1/2 = 1/4

73. What percentage of the individuals prefer beer?

P(B)=.511 51.1%

75. Do males tend to prefer beer more than females do?

P(B│M)>P(B│F)? P(B│M)=(P(B∩M))/(P(M))=(.375)/(.534)=.702 P(B│F)=(P(B∩F))/(P(F))=(.136)/(.466)=.291 Since P(B│M)>P(B│F), yes, males tend to prefer beer more than females do. (.702/.291=2.4 times more)

76. Draw a card from a deck of 52. Replace it and draw another. Find P(First card is Heart and Second card is Black)

P(First card Heart) = 13/52 = 1/4 P(Second card is Black) = 26/52 = 1/2 Since events are independent, P(First card is Heart and Second card is Black) = 1/4 X 1/2 = 1/8

69. What is the probability of selecting a female that prefers wine?

P(F∩W)=.330

74. Are the chances higher of a person being a female if we know that the person prefers wine?

P(F│W)>P(F)? P(F│W)=(P(F∩W))/(P(W))=(.330)/(.489)=.675 P(F)=.466 Since P(F│W)>P(F), yes, the chances are higher of a person being a female if we know that the person prefers wine. (.675/.466=1.4 times higher)

68. What is the probability of selecting a person that is a male and prefers beer?

P(M∩B)=.375

71. What is the probability that a randomly selected person is a male or drinks beer?

P(M∪B)=P(M)+P(B)-P(M∩B) P(M∪B)=.534+.511-.375=.670

70. What percentage of individuals do not prefer wine?

P(W^C )=P(W ̅ )=1-P(W)=1-.489=.511 51.1%

72. If a male is selected, what is the probability that he likes wine?

P(W│M)=(P(W∩M))/(P(M))=(.159)/(.534)=.298

80. Event A {Ace on first draw} Event B {Ace on second draw} Find P (A and B)

When events are independent, P (A and B) = P(A) P(B/A) P(A) = 4/52 P(B/A) = 3/51 P (A and B) = 4/52 X 3/51 = 1/221

12. What is the conditional probability that the depositor drawn is 30 or less, given that he is a male? a) 2/3 b) 7/10 c) 4/7 d) 2/5 e) none of these

a) 2/3

36. Assuming that symptoms and disease are independent, what is the probability of having a disease and symptoms, P(D∩S)? a. 0.15 b. 0.30 c. 0.40 d. 0.50

a. 0.15

38. Assuming that symptoms and disease are NOT independent, the joint probability of P(D∩S) is P(D∩S)=P(D)P(S|D). What is P(S∩D)? a. 0.15 b. 0.30 c. 0.40 d. 0.50

a. 0.15

82. If X and Y are independent events with P(X) = 0.90 and P(Y) = 0.70, then P(X∩Y) = a. 0.63 b. 0.95 c. 0.20 d. 1.60

a. 0.63

63. There are two bowls of balls. Bowl (A) has balls numbered 1 through 7. Bowl (B) has balls numbered 1 thorough 4. What is the probability of drawing a 7 from bowl (A) and a 4 from (B)? a. 1/28 b. 1/14 c. 1/7 d. 11/28

a. 1/28

65. There are two urns marked H and T. Urn H contains 2 red marbles and 1 blue marble. Urn T contains 1 red and 2 blue marbles. A coin is to be tossed. If it lands heads, a marble is drawn from Urn H. If it lands tails a marble is drawn from Urn T. Find the following probabilities: ------------------- | H | T | ----------------------------- R | 2/6 | 1/6 | 1/2 ----------------------------- B | 1/6 | 2/6 | 1/2 ----------------------------- | 1/2 | 1/2 | 1 ------------------------- a. P(heads and red) b. P(tails) c. P(red) d. P(blue) e. P(heads|red)

a. 1/3 b. 1/2 c. 1/2 d. 1/2 e. 2/3

26. P(Fish) is equal to a. 50 b. 70 c. 100 d. 130

a. 50

6. The probability of Georgia residents taking public transportation can be approximated to a binomial distribution. 30 percent of Georgia residents take public transportation. How many Georgia residents do you expect take public transportation in a sample of 20 residents? a. 6 b. 30 c. 3 d. 20

a. 6

47. A mother will be blessed with triplets. How big is the probability that the mother will give birth to two girls and one boy? a. 6/16 b. 8/16 c. 4/16 d. 1/

a. 6/16

41. Probability questions such as "what is the probability of obtaining this even and that event" typically call for the a. Multiplication rule b. Division Rule c. Subtraction Rule d. Addition Rule

a. Multiplication rule

35. Symptoms and disease are a. Mutually not exclusive b. Mutually exclusive c. Mutually conducive d. Mutually illusive

a. Mutually not exclusive

39. What is the difference between the joint probability of selecting a person with both disease and symptoms under the assumption of independence and dependence? a. There is none. b. The probability under the assumption of independence is greater. c. The probability under the assumption of independence is smaller. d. There is a difference, but it is impossible to say what it is.

a. There is none.

9. Using the previous case, the probability of obtaining at most five individuals that were born outside the U.S. in a sample of 20 is: a. f(0)+f(1)+f(2)+f(3)+f(4)+f(5) b. 1-f(x<5) c. 1-f(x≤5) d. f(6)+f(7)+f(8)+f(9)+⋯+f(18)+f(19)+f(20)

a. f(0)+f(1)+f(2)+f(3)+f(4)+f(5)

43. Probability questions such as "what is the probability of obtaining this even and that event" typically involve which sign a. ∩ b. ∪ c. ∀ d. ∈

a. ∩

11. Then P(Female) = a) 3/10 b) 2/5 c) 3/5 d) 2/3 e) none of these

b) 2/5

54. The data set represents the income levels of the members of a country club. Estimate the probability that a randomly selected member earns at least $91,000. 103,000 115,000 87,000 121,000 89,000 103,000 91,000 83,000 133,000 163,000 85,000 97,000 127,000 89,000 115,000 109,000 91,000 139,000 81,000 109,000 a. .4 b. .7 c. .8 d. .6

b. .7

57. The probability that a student will fail a statistics test is 0.32. What is the probability that this student will pass the statistics test? a. 3.13 b. 0.68 c. 0.16 d. 1.00

b. 0.68

8. Using the previous case, the probability of obtaining at least five individuals that were born outside the U.S. in a sample of 20 is: a. f(0)+f(1)+f(2)+f(3)+f(4)+f(5) b. 1-f(x<5) c. 1-f(x≤5) d. f(6)+f(7)+f(8)+f(9)+⋯+f(18)+f(19)+f(20)

b. 1-f(x<5)

55. When using a single die, what is the probability of rolling and odd number? a. 2 b. 1/2 c. 1/3 d. 1/4

b. 1/2

58. When a single card is drawn from an ordinary 52-card deck, find the probability of getting red king? a. 1/13 b. 1/26 c. 1/52 d. 1/4

b. 1/26

56. A bag contains 3 red marbles, 5 blue marbles, and 4 green marbles. What is the probability of choosing a red marble? a. 5/8 b. 1/4 c. 5/12 d. 1/3

b. 1/4

20. How many elements are in M∩N? 1 2 3 4

b. 2

17. The probability of selecting a male with no health insurance is: a. 2 b. 2/10 c. 2/5 d. Other

b. 2/10

61. A bag contains 15 balls numbered 1 through 15. What is the probability of selecting a ball that has an odd number and is divisible by 5? a. 7 b. 2/15 c. 15/7 d. 7/15

b. 2/15

48. A mother will be blessed with triplets. How big is the probability that the mother will give birth first to a girl, then a boy, and then again a girl? a. 1/16 b. 2/16 c. 3/16 d. 4/16

b. 2/16

52. A bag contains 6 red marbles, 3 blue marbles, and 7 green marbles. If a marble is randomly selected from the bag, what is the probability that it is blue? a. 1/3 b. 3/16 c. c. 1/13 d. d. 1/7

b. 3/16

Out of hundred people asked, 70 answered that they eat beef, 50 eat fish, and 10 are vegan. Therefore, 90 eat meat (in this case beef and fish are considered meat). Complete the Venn diagram. 25. P(Beef) is equal to a. 50 b. 70 c. 100 d. 130

b. 70

46. A mother will be blessed with triplets. How big is the sample space of the children's gender combinations? a. 6 b. 8 c. 9 d. 16

b. 8

iPhone Android Total <25 0.140 0.240 0.380 25+ 0.430 0.190 0.620 Total 0.570 0.430 1.000 P(<25 | iPhone)=P(<25 ∩ iPhone)/P(iPhone) =.140/.570=.246 Based on the previous data, what percent of the sample are either iPhone users or users that are less than 25 years old? a. 26% b. 81% c. 9% d. 18%

b. 81%

18. The number of individuals that are males or individuals that have insurance is: a. 3 b. 9 c. 12 d. Other

b. 9

59. Assume you want to find the probability of getting a queen or a heart from a single card draw from an ordinary 52-card deck. Then, the events "Queen" and "Heart" are said to be a. Mutually exclusive b. Mutually not exclusive c. Mutually inclusive d. Mutually not inclusive

b. Mutually not exclusive

31. What's the probability that someone eats meat, either beef (A) or fish (B)? a. P(A∩B) b. P(A∪B) c. P(AB) d. P(AB)

b. P(A∪B)

83. If P(A) = 0.25, P(A│Y) = 0.35, and P(A│X) = 0.10, then events A and Y a. are independent b. are dependent c. could be either independent or dependent, depending on the value of Y d. could be either independent or dependent, depending on the value of X

b. are dependent

44. Probability questions such as "what is the probability of obtaining this even or that event" typically involve which sign a. ∩ b. ∪ c. ∀ d. ∈

b. ∪

(Questions 16-22 are based on the following) A sample of 10 individuals provided the following information: Health Insurance H No Health Insurance N Male M 3 2 Female F 4 1 16. What is the probability of selecting a male? a. .3 b. .03 c. .5 d. 30%

c. .5

53. A polling firm, hired to estimate the likelihood of the passage of an upcoming referendum, obtained the set of survey responses to make its estimate. The encoding system for the data is: 1 = FOR, 2 = AGAINST. If the referendum were held today, estimate the probability that it would pass. 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1 a. .5 b. .65 c. .6 d. .4

c. .6

86. If P(A) = 0.50, P(B) = 0.40, then, and P(A ∪ B) = 0.88, then P(B | A) = a. 0.02 b. 0.03 c. 0.04 d. 0.05

c. 0.04

84. If P(A) = 0.48, P(A ∪ B) = 0.82, and P(B) = 0.54, then P(A ∩ B) = a. 0.3936 b. 0.3400 c. 0.2000 d. 1.0200

c. 0.2000

3. Consider the experiment of inspecting light bulbs in a lot of 200 bulbs. We are interested in the number of defective bulbs in the lot. Historically these lots have on average one defective bulb per lot. The lot is rejected if the number of defective items is greater than or equal to 3. What is the probability of rejecting a lot? a. f(0) + f(1) + f(2) + f(3) b. 1 - f(x<=3) c. 1 - f(x<=2) d. Other

c. 1 - f(x<=2)

50. On a multiple choice test, each question has 4 possible answers. If you make a random guess on the first question, what is the probability that you are correct? a. 4 b. 1 c. 1/4 d. 0

c. 1/4

45. A sample space consists of 80 separate events that are equally likely. What is the probability of each? a. 1 b. 0 c. 1/80 d. 80

c. 1/80

60. The probability of drawing a queen or a heart from an ordinary 52-card deck is a. 8/52 b. 12/52 c. 16/52 d. 17/52

c. 16/52

2. Consider the experiment of inspecting light bulbs in a lot of 200 bulbs. We are interested in the number of defective bulbs in the lot. Historically these lots have on average one defective bulb per lot. How many possible values can the random variable take? a. 1 b. 200 c. 201 d. Other

c. 201

30. From the addition rule of independent events, which is P(Beef∪Fish)=P(Beef)+P(Fish)-P(Beef∩Fish), it follows that P(Beef∩Fish) is a. 10 b. 20 c. 30 d. 40

c. 30

19. As a two-step experiment, how many possible outcomes does the sample space have? a. 2 b. 3 c. 4 d. None of the above

c. 4

14. A local trade union consists of plumbers and electricians. Classified according to rank: Apprentice Journeyman Master ------------------------------------ Plumbers 25 | 20 | 30 75 ------------------------------------ Electricians 15 | 40 | 20 75 ------------------------------------- 40 60 50 A member of the union is selected at random. Given that the person selected is a plumber, the probability that he is a journeyman is: a. 1/2 b. 1/3 c. 4/15 d. 2/15 e. none of these.

c. 4/15

51. A die with 12 sides is rolled. What is the probability of rolling a number less than 11? a. 1/12 b. 10 c. 5/6 d. 11/12

c. 5/6

29. From the addition rule of independent events, which is P(Beef∪Fish)=P(Beef)+P(Fish)-P(Beef∩Fish), it follows that P(Beef∪Fish) is a. 50 b. 70 c. 90 d. 110

c. 90

49. A mother will be blessed with triplets. How big is the probability that the mother will give birth to at least one boy? a. 1-P(All girls) b. 7/8 c. Answers a. and b. are correct d. None of the above.

c. Answers a. and b. are correct

Select the correct option that represents "A given B": a. A∩B b. B|A c. A|B d. A∪B

c. A|B

27. P(Vegan') is equal to a. P(Beef∪Fish) b. 90 c. Both a. and b. d. None of the above.

c. Both a. and b.

21. Events H and N are ______. a. Independent and mutually exclusive b. Independent and not mutually exclusive c. Dependent and mutually exclusive d. Dependent and not mutually exclusive

c. Dependent and mutually exclusive

4. Consider the experiment of selling a breakfast cereal brand at a local store during a particular week. Let x denote the number of boxes sold during the week. Based on the table provided below select the correct statement: # Boxes sold in a week # of Weeks [out of 100 weeks] 0 5 1 20 2 30 3 20 4 15 5 5 6 5 Total 100 a. The random variable has 7 possible experimental outcomes. The random variable is continuous. b. The random variable has 6 possible experimental outcomes. The random variable is discrete. c. The random variable has 7 possible experimental outcomes. The random variable is discrete. d. The random variable has 6 possible experimental outcomes. The random variable is continuous.

c. The random variable has 7 possible experimental outcomes. The random variable is discrete.

1. A random variable that can assume only a finite number of values is referred to as a(n) a. infinite sequence b. finite sequence c. discrete random variable d. discrete probability function

c. discrete random variable

The depositors at Save-More Bank are categorized by age and sex. We are going to select an individual at random from this group of 2000 depositors. Sex Age | Male | Female ------------------------------------- 30 or less | 800 | 600 31 or more | 400 | 200 ------------------------------------- 9. Then P(Female30 or less) = a) 2/5 b) 3/4 c) 3/7 d) 3/10 e) none of these

d) 3/10

10. Then P[Male or (31 or more)] = a) 1/5 b) 3/10 c) 1/2 d) 7/10 e) none of these

d) 7/10

88. A random sample of 100 individuals showed the Smartphone ownership by age group (see below). If an iPhone user is selected, what is the probability that the user is <25? iPhone Android Total <25 14 24 38 25+ 43 19 62 Total 57 43 100 a. .09 b. .40 c. 1.4 d. .246

d. .246

What is the probability of N-complement P(N ̅)? 2 .2 .3 .7

d. .7

87. If A and B are independent events with P(A) = 0.38 and P(B) = 0.55, then P(A | B) = a. 0.209 b. 0.000 c. 0.550 d. 0.38

d. 0.38

85. If A and B are independent events with P(A) = 0.35 and P(B) = 0.20, then, P(A ∪ B) = a. 0.07 b. 0.62 c. 0.55 d. 0.48

d. 0.48

37. Assuming that symptoms and disease are NOT independent, the joint probability of P(D∩S) is P(D∩S)=P(D)P(S|D). What is P(S|D)? a. 0.20 b. 0.30 c. 0.40 d. 0.50

d. 0.50

7. Ten percent of the population in the state of Georgia was born outside the United States. Assuming a binomial distribution, how many individuals in a sample of 20 are expected to have been born IN the U.S.? a. .10 b. .90 c. 2 d. 18

d. 18

42. Probability questions such as "what is the probability of obtaining either this event or that event" typically call for the a. Multiplication rule b. Division Rule c. Subtraction Rule d. Addition Rule

d. Addition Rule

33. Given that someone eats meat, what's the probability that someone eats fish? a. P(Fish|Meat) b. P(Fish∩Meat)/P(Meat) c. 50/90 d. All of the above.

d. All of the above

34. Given that someone is not a vegan, what is the probability that someone eats meat? a. P(Meat|Vegan') b. P(Meat∩Vegan')/P(Vegan')=P(Meat)P(Vegan'|Meat) /P(Vegan') c. 1 d. All of the above.

d. All of the above.

32. What's the probability that someone eats beef (A) and fish (B)? a. P(A∪B) b. P(A∩B) c. 30 d. Both b. and c.

d. Both b. and c.

40. Because the probability of having Statisis given that someone has Statisis symptoms is not any different than the probability of having Statisis without any knowledge about possible symptoms suggests that, statistically, symptoms and disease are _____ and _____. a. Dependent, mutually exclusive b. Dependent, mutually not exclusive c. Independent, mutually exclusive d. Independent, mutually not exclusive

d. Independent, mutually not exclusive

28. Are eating beef or fish mutually exclusive events? a. Depends on whether the fish has bones. b. Yes always. c. Only if the fish is served in a white wine sorbet sauce with freshly cut basil and the beef is grilled medium-rare. d. No.

d. No.

81. If A and B are independent events, then a. P(A) must be equal to P(B) b. P(A) must be greater than P(B) c. P(A) must be less than P(B) d. P(A) must be equal to P(A│B)

d. P(A) must be equal to P(A│B)

A random sample of 100 individuals showed the Smartphone ownership by age group (see below). If an iPhone user is selected, what is the probability that the user is 25 or older? iPhone Android Total <25 18 24 42 25+ 43 15 58 Total 61 39 100 a. .705 .31 .02 .18 iPhone Android Total <25 0.180 0.240 0.420 25+ 0.430 0.150 0.580 Total 0.610 0.390 1.000 P(25+ | iPhone)=P(25+ ∩ iPhone)/P(iPhone) =.430/.610=.705 Based on the previous data, what percent of the sample are either iPhone users or users that are 25 or older? a. 12% b. 3% c. 50% d. 76%

d. P(iPhone ∪ 25+)=P(iPhone)+P(25+)-P(iPhone ∩ 25+)=.61+.58-.43=.76 or 76%

5. Which of the following is a required condition for a discrete probability function? a. ∑f(x) = 0 for all values of x b. f(x) 1 for all values of x c. f(x) < 0 for all values of x d. ∑f(x) = 1 for all values of x

d. ∑f(x) = 1 for all values of x