EF 507PS-Chapter 4FALL 2008
1. Suppose you roll a pair of dice. Let A be the event that you roll an even number. Let B be the event that you roll an odd number. Which of the following statements is true?
A)The events A and Bare not mutually exclusive.
B)The intersection of A and Bis the empty set.
C)The events A and Bare not collectively exhaustive.
D)The complement of event B is the set [1, 3, 5, 7, 9, 11].
ANSWER:B
2. Which of the following statements is always true for any two events A and Bdefined on a sample space S?
A)If the complement of event A is the empty set, then event A is the sample space S.
B)If the union of events A and Bis not the empty set, then.
C)If events A and Bare mutually exclusive, then.
D)If events A and Bare collectively exhaustive, then.
ANSWER:A
QUESTIONS 3 THROUGH 5 ARE BASED ON THE FOLLOWING INFORMATION:
The finishing process on new furniture leaves slight blemishes. The table shown below displays a manager’s probability assessment of the number of blemishes in the finish of new furniture.
Number of Blemishes / 0 / 1 / 2 / 3 / 4 / 5Probability / 0.34 / 0.25 / 0.19 / 0.11 / 0.07 / 0.04
3.Let event A be that there are more than three blemishes and let event B be that there are four or fewer blemishes. Which of the following statements is true?
A)P() = 0.18.
B)P() = 0.07.
C)Events A and B are collectively exhaustive.
D)Events A and B are mutually exclusive.
ANSWER:C
4.Let event A be that there are more than two blemishes and let event B be that there are four or fewer blemishes. Which of the following statements is true?
A)P() = 0.18.
B)P() = 0.07.
C)P() = 0.58.
D)P() = 0.89.
ANSWER:A
5.Let A be the event that there is at least one blemish and let event B be that there at most three blemishes. Which of the following statements is true?
A)P() = 0.18.
B)P() = 0.55.
C)P() = 0.30.
D)P() = 0.96.
ANSWER:A
6.The probability that an employee at a company uses illegal drugs is 0.08. The probability than an employee is male is 0.55. Assuming that these events are independent, what is the probability that a randomly chosen employee is a male drug user?
A)0.742
B)0.145
C)0.044
D)0.006
ANSWER:C
7.The purchasing agent for a municipality has contracted with a local car dealer to purchase four cars. The dealer has 25 cars on his lot; 10 red, 7 blue, 6 white and 2 purple. If the purchasing agent has no control over the colors he receives, what is the probability that he receives at least one of the purple cars?
A)0.33
B)0.30
C)0.36
D)0.39
ANSWER:B
8.A recent survey found that 14% of secretaries have experienced some form of wrist pain from typing. 6% of all secretaries have both experienced some form of wrist pain from typing and taken aspirin on a daily basis. What is the probability that a secretary who has wrist pain takes aspirin on a daily basis?
A)0.429
B)0.915
C)0.571
D)0.085
ANSWER:A
QUESTIONS 9 THROUGH 12 ARE BASED ON THE FOLLOWING INFORMATION:
A survey of recent e-commerce start-up firms was undertaken at an industry convention. Representatives of the firm where asked for the geographic location of the firm as well as the firm’s outlook for growth in the coming year. The results are provided below.
RegionNortheast / South / Midwest / West
Low / 0.04 / 0.12 / 0.14 / 0.19
Expected Growth / Medium / 0.05 / 0.08 / 0.06 / 0.12
High / 0.03 / 0.05 / 0.08 / 0.04
9.What is the probability that one of these start-up firms was from the Northeast?
A)0.04
B)0.12
C)0.49
D)0.33
ANSWER:B
10.Are the events “firm from the South” and “expects high growth” statistically independent?
A)Yes
B)No
C)Unable to tell from the data
D)Maybe
ANSWER:A
11.If the firm interviewed was from the West, what is the probability that it expected medium or high growth?
A)0.24
B)0.35
C)0.16
D)0.46
ANSWER:D
12.If the firm interviewed was expecting medium or high growth, what is the probability of the firm being located in the West?
A)0.16
B)0.31
C)0.46
D)0.27
ANSWER:B
13.Consider two events A and B. Which of the following statements is true?
A)If the probability of A given B is 0.4, then the probability of A given the complement of B is 0.6.
B)If the probability of A given B is 0.4, then the probability of the complement of A given the complement of B is 0.6.
C)If the probability of A given B is 0.4, then the probability of the complement of A given B is 0.6
D)If the probability of A given B is 0.4 and the probability of A is 0.4, then events A and B are mutually exclusive.
ANSWER:C
QUESTIONS 14 THROUGH 15 ARE BASED ON THE FOLLOWING INFORMATION:
In a recent survey of college students, students where asked about their use of the Internet for research. The information was displayed in the table below. Let A be the event that the student was a business major. Let B be the event that the student uses the Internet for research.
Use Internet for research / Don’t Use InternetBusiness Students / 0.38 / 0.22
Education Students / 0.25 / 0.15
14.Which of the following is true?
A)P(A | B) < P(B | A).
B)P(A | ) > P(B |).
C)P(AB) = 0.85.
D)Events A and B are statistically independent.
ANSWER:A
15. Which of the following is true?
A)P(A | B) = 0.81
B)P(A) = 0.16
C)Events A and B are statistically independent.
D)P( | ) = 0.375
ANSWER:D
16.The probability that a new small business closes before the end of its first year is 42%. In addition, 37% of all new businesses are started by women. The probability that a new business is either owned by a woman or goes out of business is 62%. Your sister wants to start a new business. What is the probability her business is still open at the end of the first year?
ANSWER:
A = A new small business closes before the end of its first year.
B = New business started by a woman.
B / / TotalA / 0.17 / 0.25 / 0.42
/ 0.20 / 0.38 / 0.58
Total / 0.37 / 0.63 / 1.00
17The probability that a person has an Internet connection at home is 34%. The probability that they have access to the Internet at work is 40%. The probability that a person who has access to the Internet at work also has access at home is 55%. What is the probability that a person with an Internet connection at home also has one at work?
ANSWER:
H = Internet at home
W = Internet at work
P(H) = 0.34, P(W) = 0.40, P(H | W) = 0.55.
Hence, P(HW) =P(H/W)P(W) = (0.55)(0.40) = 0.22, and
P(W | H) = P(WH)/P(H) =0.22/0.34 = 0.647.
QUESTIONS 18 THROUGH 26 ARE BASED ON THE FOLLOWING INFORMATION:
A publisher sends advertising materials for an economics text to 75% of all professors teaching the appropriate economics course. Twenty eight percent of the professors who received this material adopted the book, as did 8% of the professors who did not receive the material. Define the following events of interest:
= Professor receives advertising material
= Professor does not receive advertising material
= Professor adopts the book
= Professor does not adopt the book
18.What is the probability that a professor who adopts the book has received the advertising material?
ANSWER:
= 0.75, = 1 - 0.75 = 0.25, = 0.28, = 0.08
Using Bayes’ Theorem, we get
19.What is the probability that a professor who adopts the book has not received the advertising material?
ANSWER:
Using Bayes’ Theorem, we get
Also, since, then 1 – 0.913 = 0.087
20.What is the probability that a professor who receives advertising material has not adopted the book?
ANSWER:
, then 1 – 0.28 = 0.72
21.What is the probability that a professor who does not receive advertising material has not adopted the book?
ANSWER:
, then 1 – 0.08 = 0.92
22.What is the probability that a professor receives advertising material and has adopted the book?
ANSWER:
(0.28)(0.75) = 0.21
23.What is the probability that a professor receives advertising material and has not adopted the book?
ANSWER:
(0.72)(0.75) = 0.54
24.What is the probability that a professor does not receive advertising material and has adopted the book?
ANSWER:
(0.08)(0.25) = 0.02
25.What is the probability that a professor does not receive advertising material and has not adopted the book?
ANSWER:
(0.92)(0.25) = 0.23
26.What is the probability that a professor adopts the book?
ANSWER:
0.21 + 0.02 = 0.23
27.What is the probability that a professor does not adopt the book?
ANSWER:
0.54 + 0.23 = 0.77
Also, since, then1 – 0.23 = 0.77
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