qmb 2100 basic business statistics - spring 2014 - practice test #2b

1

QMB 2100 Basic Business Statistics – Spring 2014

Practice Test #2 B

1. The complement of P(A | B) is

a. P(AC | B)

b. P(A | BC)

c. P(B | A)

d. P(A ∩ B)

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

a. addition law

b. subtraction law

c. multiplication law

d. division law

3. If A and B are mutually exclusive, then

a. P(A) + P(B) = 0

b. P(A) + P(B) = 1

c. P(A ∩ B) = 0

d. P(A ∩ B) = 1

4. The range of probability is

a. any value larger than zero

b. any value between minus infinity to plus infinity

c. zero to one

d. any value between -1 to 1

5. In statistical experiments, each time the experiment is repeated

a. the same outcome must occur

b. the same outcome cannot occur again

c. a different outcome may occur

d. None of the other answers is correct.

6. The set of all possible sample points (experimental outcomes) is called

a. a sample

b. an event

c. the sample space

d. a population

7. The sample space refers to

a. any particular experimental outcome

b. the sample size minus one

c. the set of all possible experimental outcomes

d. both any particular experimental outcome and the set of all possible experimental outcomes

are correct

2

8. An experiment consists of tossing 4 coins successively. The number of sample points in this

experiment is

a. 16

b. 8

c. 4

d. 2

9. 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

a. 30

b. 100

c. 729

d. 1,000

10. 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

a. 2

b. 4

c. 6

d. 8

11. Assume your favorite football team has 2 games left to finish the season. The outcome of each

game can be win, lose or tie. The number of possible outcomes is

a. 2

b. 4

c. 6


12. Each customer entering a department store will either buy or not buy some merchandise. An

experiment consists of following 3 customers and determining whether or not they purchase any

merchandise. The number of sample points in this experiment is

a. 2

b. 4

c. 6

d. 8

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

a. bar chart

b. pie chart

c. histogram


3

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

selections are there?

a. 20

b. 7

c. 5

d. 10

15. 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?

a. 302,400

b. 720

c. 1,814,400

d. 10

16. When the assumption of equally likely outcomes is used to assign probability values, the method

used to assign probabilities is referred to as the

a. relative frequency method

b. subjective method

c. probability method

d. classical method

17. A method of assigning probabilities that assumes the experimental outcomes are equally likely is

referred to as the

a. objective method

b. classical method

c. subjective method

d. experimental method

18. 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

a. relative frequency method

b. subjective method

c. classical method

d. posterior method

19. The probability assigned to each experimental outcome must be

a. any value larger than zero

b. smaller than zero

c. one

d. between zero and one

4

20. An experiment consists of four outcomes with P(E1) 0.2, P(E2) 0.3, and P(E3) 0.4. The

probability of outcome E4 is

a. 0.500

b. 0.024

c. 0.100

d. 0.900

21. A graphical method of representing the sample points of a multiple-step experiment is

a. a frequency polygon

b. a histogram

c. an ogive

d. a tree diagram

22. A(n) __________ is a graphical representation in which the sample space is represented by a

rectangle and events are represented as circles.

a. frequency polygon

b. histogram

c. Venn diagram

d. tree diagram

23. Given that event E has a probability of 0.25, the probability of the complement of event E

a. cannot be determined with the above information

b. can have any value between zero and one

c. must be 0.75

d. is 0.25

24. The symbol shows the

a. union of events

b. intersection of events

c. sum of the probabilities of events

d. sample space

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

a. all the sample points common to both A and B

b. all the sample points belonging to A or B

c. all the sample points belonging to A or B or both

d. all the sample points belonging to A or B, but not both

26. The probability of the union of two events with nonzero probabilities

a. cannot be less than one

b. cannot be one

c. cannot be less than one and cannot be one


5

27. The symbol ∩ shows the

a. union of events

b. intersection of events

c. sum of the probabilities of events


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

a. independent events

b. the intersection of two events

c. the union of two events

d. conditional events

If P(A) 0.38, P(B) 0.83, and P(A B) 0.57; then P(A B)

a. 1.21

b. 0.64

c. 0.78

d. 1.78

If P(A) 0.62, P(B) 0.47, and P(A B) 0.88; then P(A B)

a. 0.2914

b. 1.9700

c. 0.6700

d. 0.2100

If P(A) 0.85, P(A B) 0.72, and P(A B) 0.66, then P(B)

a. 0.15

b. 0.53

c. 0.28

d. 0.15

32. Two events are mutually exclusive if

a. the probability of their intersection is 1

b. they have no sample points in common

c. the probability of their intersection is 0.5

d. the probability of their intersection is 1 and they have no sample points in common

33. Events that have no sample points in common are

a. independent events

b. posterior events

c. mutually exclusive events

d. complements

6

34. The probability of the intersection of two mutually exclusive events

a. can be any value between 0 to 1

b. must always be equal to 1

c. must always be equal to 0

d. can be any positive value

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

a. will be equal to zero

b. can have any value larger than zero

c. must be larger than zero, but less than one

d. will be one

36. 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

a. one

b. any positive value

c. zero

d. any value between 0 to 1

If A and B are mutually exclusive events with P(A) 0.3 and P(B) 0.5, then P(A B)

a. 0.30

b. 0.15

c. 0.00

d. 0.20

If A and B are mutually exclusive events with P(A) 0.3 and P(B) 0.5, then P(A B)

a. 0.00

b. 0.15

c. 0.8

d. 0.2

39. In an experiment, events A and B are mutually exclusive. If P(A) 0.6, then the probability of B

a. cannot be larger than 0.4

b. can be any value greater than 0.6

c. can be any value between 0 to 1

d. cannot be determined with the information given

40. Which of the following statements is(are) always true?

a. -1 P(Ei) 1

b. P(A) 1 P(Ac)

c. P(A) P(B) 1

d. both P(A) 1 P(Ac) and P(A) P(B) 1

7

41. One of the basic requirements of probability is

a. for each experimental outcome Ei, we must have P(Ei) 1

b. P(A) P(Ac) 1

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

d. both P(A) P(Ac) 1 and if there are k experimental outcomes, then P(E1) P(E2) ...

P(Ek) 1

42. Events A and B are mutually exclusive with P(A) 0.3 and P(B) 0.2. The probability of the

complement of Event B equals

a. 0.00

b. 0.06

c. 0.7


43. The multiplication law is potentially helpful when we are interested in computing the probability

of

a. mutually exclusive events

b. the intersection of two events

c. the union of two events


If P(A) 0.80, P(B) 0.65, and P(A B) 0.78, then P(BA)

a. 0.6700

b. 0.8375

c. 0.9750

d. Not enough information is given to answer this question.

45. If two events are independent, then

a. they must be mutually exclusive

b. the sum of their probabilities must be equal to one

c. the probability of their intersection must be zero


If A and B are independent events with P(A) 0.38 and P(B) 0.55, then P(AB)

a. 0.209

b. 0.000

c. 0.550


If X and Y are mutually exclusive events with P(X) 0.295, P(Y) 0.32, then P(XY)

a. 0.0944

b. 0.6150

c. 1.0000

d. 0.0000

8

48. Two events with nonzero probabilities

a. can be both mutually exclusive and independent

b. cannot be both mutually exclusive and independent

c. are always mutually exclusive

d. cannot be both mutually exclusive and independent and are always mutually exclusive

49. If P(A) 0.50, P(B) 0.60, and P(A B) 0.30; then events A and B are

a. mutually exclusive events

b. not independent events

c. independent events


50. On a December day, the probability of snow is 0.30. The probability of a "cold" day is .50. The

probability of snow and a "cold" day is 0.15. Are snow and "cold" weather independent events?

a. only if given that it snowed

b. no

c. yes

d. only when they are also mutually exclusive

51. If P(A) 0.5 and P(B) 0.5, then P(A B) is

a. 0.00

b. 0.25

c. 1.00

d. cannot be determined from the information given

If A and B are independent events with P(A) 0.4 and P(B) 0.6, then P(A B)

a. 0.76

b. 1.00

c. 0.24

d. 0.2


a. 0.62

b. 0.12

c. 0.60

d. 0.68


a. 0.65

b. 0.55

c. 0.10


9

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

a. A and B are also independent.

b. P(A B) P(A)P(B)

c. P(A B) P(A) P(B)

d. P(A B) P(A) P(B)

If A and B are independent events with P(A) 0.05 and P(B) 0.65, then P(AB)

a. 0.05

b. 0.0325

c. 0.65

d. 0.8

57. A six-sided die is tossed 3 times. The probability of observing three ones in a row is

a. 1/3

b. 1/6

c. 1/27

d. 1/216

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

a. P(B|A) = 0.7

b. P(AC|B) = 0.7

c. P(A|BC) = 0.7

d. P(AC|B

C) = 0.7

59. If A and B are independent events with P(A) = 0.1 and P(B) = 0.4, then

a. P(A B) = 0

b. P(A B) = .04

c. P(A B) = 0.5

d. P(A B) = 0.25

60. If P(A|B) = 0.3 and P(B) = 0.8, then

a. P(A) = .24

b. P(B|A) = 0.7

c. P(A B) = 0.5

d. P(A B) = 0.24

61. If P(A) = 0.6, P(B) = 0.3, and P(A B) = 0.2, then P(B|A) =

a. 0.33

b. 0.5

c. 0.67

d. 0.9

10

ANSWER KEY

1. A

2. C

3. C

4. C

5. C

6. C

7. C

8. A

9. D

10. D

11. D

12. D

13. D

14. D

15. B

16. D

17. B

18. A

19. D

20. C

21. D

22. C

23. C

24. A

25. C

26. D

27. B

28. C

29. B

30. D

31. B

32. B

33. C

34. C

35. A

36. C

37. C

38. C

39. A

40. B

41. C

42. D

43. B

44. B

45. D

46. D

47. D

48. B

49. C

11

50. C

51. D

52. C

53. D

54. B

55. C

56. A

57. D

58. B

59. B

60. D

61. A

qmb 2100 basic business statistics - spring 2014 - practice test #2b

Documents