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Chapter Four Practice Exercises Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Let A and B be events with P(A) = 0.4, P(B) = 0.9, and P(A and B) = 0.32. Are A and B mutually exclusive? A) No B) Yes
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2) A section of an exam contains two multiple-choice questions, each with three answer choices (listed "A", "B", and "C"). Assuming the outcomes to be equally likely, find the probability (as a reduced fraction) that at least one answer is "A". [Hint: List all the outcomes of the sample space first.] A) 5/9 B) 2/3 C) 7/9 D) 1/3
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3) Let E be the event that a corn crop has an infestation of ear worms, and let B be the event that a corn crop has an infestation of corn borers.
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Suppose that P(E) = 0.23, P(B) = 0.11, and P(E and B) = 0.05. Find the probability that a corn crop has no corn borer infestation. A) 0.89 B) 0.66 C) 0.29 D) 0.77 Solve the problem. Round your answer, as needed. 4) In a business class, 25% of the students have never taken a statistics class, 55% have taken only one semester of statistics, and the rest have taken two or more semesters of statistics. The professor randomly assigns students to groups of three to work on a project for the course. What is the probability that neither of your two group mates has studied statistics? A) 0.063 B) 0.25 C) 0.75 D) 0.20 E) 0.50
5) Opinion-polling organizations contact their respondents by sampling random telephone
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numbers. Assume that interviewers can now reach about 77% of U.S. households, while the percentage of those contacted who agree to cooperate with the survey is 34%. Each household, of course, is independent of the others. What is the probability of obtaining an interview with the next household on the sample list? A) 0.078 B) 0.508 C) 0.262 D) 0.152 E) 0.770
6) The date is March 9, and there are 108 people in a room. What is the probability that at least one of them has a birthday today? A) 0.744 B) 0.742
C) 0.296
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D) 0.258
E) 0.256
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7) Opinion-polling organizations contact their respondents by sampling random telephone
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numbers. Assume that interviewers can now reach about 77% of U.S. households, while the percentage of those contacted who agree to cooperate with the survey is 35%. Each household, of course, is independent of the others. What is the probability that the next household on the list will be contacted but will refuse to cooperate? A) 0.177 B) 0.501 C) 0.081 D) 0.150 E) 0.270
8) There is a huge pile of buttons in which 29% are black, 11% are blue, 17% are orange, 24% are
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white, and the rest are clear. You close your eyes, choose a button at random, write down what color it is, and then put it back in the pile. What is the probability that the third button you choose is the first one thatʹs clear? A) 0.029 B) 0.531 C) 0.007 D) 0.157 E) 0.125
9) You roll a fair die three times. What is the probability that you roll all 2ʹs? A) 0.5 B) 1.5 C) 0.333 D) 0.005
9) E) 0.167
Solve the problem. 10) At a California college, 22% of students speak Spanish, 5% speak French, and 3% speak both languages. What is the probability that a student chosen at random from the college speaks Spanish but not French? A) 0.17 B) 0.19 C) 0.24 D) 0.02 E) 0.2
11) In a business class, 33% of the students have never taken a statistics class, 42% have taken only
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one semester of statistics, and the rest have taken two or more semesters of statistics. The professor randomly assigns students to groups of three to work on a project for the course. What is the probability that the first group mate you meet has studied no more than one semester of statistics? A) 0.58 B) 0.42 C) 0.25 D) 0.75 E) 0.33
12) In a business class, 35% of the students have never taken a statistics class, 10% have taken only
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one semester of statistics, and the rest have taken two or more semesters of statistics. The professor randomly assigns students to groups of three to work on a project for the course. What is the probability that the first group mate you meet has studied two or more semesters of statistics? A) 0.10 B) 0.45 C) 0.65 D) 0.90 E) 0.55
13) The probability that a student at a certain college is male is 0.45. The probability that a student at that college has a job off campus is 0.33. The probability that a student at the college is male and has a job off campus is 0.15. If a student is chosen at random from the college, what is the probability that the student is male or has an off campus job? A) 0.47 B) 0.93 C) 0.63 D) 0 E) 0.78
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14) An Imaginary Poll in April 2005 asked 931 U.S. adults what their main source of news was:
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newspapers, television, internet, or radio? Here are the results: Response Number Newspapers 242 Television 398 Internet 126 Radio 165 Total 931 If we select a person at random from this sample of 931 adults, what is the probability that the person responded ʺNewspapersʺ? A) 0.242 B) 0.177 C) 0.260 D) 0.427 E) 0.135
15) In a survey of American women who were asked to name their favorite color, 18% said blue, 19%
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said red, 18% said green, 12% said yellow, 11% said black, and the rest named another color. If you pick a survey participant at random, what is the probability that her favorite color is not blue? A) 0.18 B) 0.82 C) 0.8 D) 0.60 E) 0.72
16) For the event described below, which of the following represents the complement of the event. A sample of 471 software DVDs was selected. Exactly 34 of these were defective. A) Exactly 34 DVDs were not defective. B) No more than 34 DVDs were defective. C) Exactly 437 DVDs were not defective. D) The number of defective DVDs was not equal to 34.
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17) What is the correct relationship between events A and B: A: Laura participated in an out-of-town volleyball game at 11:00 AM last Friday. B: Laura met with her academic advisor on campus at 11:00 AM last Friday.
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A) A and B are mutually exclusive. C) A and B are not mutually exclusive.
B) A and B are complementary. D) If B is true, A is true.
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18) A survey asked 33,083 homeowners how many pets they owned. The results were as followed: Number of Pets 0 1 2 3 4 or more Total
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Number of Homeowners 5476 11,229 10,546 5147 685 33,083
What is the probability that a sampled homeowner has more than 1 pet? A) 0.176 B) 0.505 C) 0.495 D) 0.166 19) Assume a soldier is selected at random from the Army. Determine whether the events A and B are independent, mutually exclusive, or neither. A: The soldier is a corporal. B: The soldier is a colonel. A) independent B) neither
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C) mutually exclusive
20) For this year's mayoral election, voter dissatisfaction is very high. In a survey of 500 20) likely voters, 210 said they planned to write in an independent candidate rather than vote for the Democrat or Republican candidate for mayor. What is the probability that a surveyed voter plans to write in an independent candidate? A) 0.42 B) 0.5 C) 0.21 D) 0.58 21) In a poll of 451 university students, 193 said that they were opposed to legalizing marijuana. What is the probability that a surveyed student opposes legalization of marijuana? A) 0.428 B) 0.748 C) 0.572 D) 0.252
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22) What is the correct relationship between events A and B: A: Kathleen made an A on her Biology final exam. B: Kathleen did not make an A on the Biology final exam.
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A) A and B are mutually exclusive. C) A and B are not mutually exclusive.
B) A and B are complementary. D) If B is untrue, A is untrue.
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23) What is the correct relationship between events A and B: A: Karl is college graduate. B: Karl is a high school graduate. A) A and B are mutually exclusive. C) A and B are not mutually exclusive.
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B) B is the complement of A. D) If B is not true, A cannot be true.
24) Let E be the event that a corn crop has an infestation of ear worms, and let B be the event that a corn crop has an infestation of corn borers.
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Suppose that P(E) = 0.18, P(B) = 0.18, and P(E and B) = 0.12. Find the probability that a corn crop has either an ear worm infestation, a corn borer infestation, or both. A) 0.12 B) 0.48 C) 0.24 D) 0.64 25) In a recent semester at a local university, 520 students enrolled in both General Chemistry and Calculus I. Of these students, 88 received an A in general chemistry, 76 received an A in calculus, and 31 received an A in both general chemistry and calculus.
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Find the probability that a randomly chosen student received an A in general chemistry o calculus or both. A) 0.375 B) 0.315 C) 0.256 D) 0.811 Find the indicated probability. 26) The table shows the political affiliation of voters in one city and their positions on stronger gun control laws. Stronger Gun Control Favor Oppose Republican 0.11 0.27 Democrat 0.25 0.16 Other 0.15 0.06
What is the probability that a Democrat opposes stronger gun control laws? A) 0.160 B) 0.390 C) 0.490 D) 0.327
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E) 0.410
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27) The contingency table below provides a joint frequency distribution
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for a random sample of patients at a hospital classified by blood type and sex.
103
86
25
11
225
74
71
14
6
165
177
157
39
17
390
If a person is selected at random from the sample, find the probability that the person has blood type A or is female. A) 0.221 B) 0.382 C) 0.548 D) 0.759 E) 0.979
28) College students were given three choices of pizza toppings and asked to choose one favorite.
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The following table shows the results. toppings freshman sophomore junior senior cheese
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16
20
21
meat
22
21
16
15
veggie
16
15
22
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If a student responded ʺmeatʺ, what is the probability that they are a junior?\ A) 0.073
B) 0.276 C) 0.216 D) 0.16 E) 0.301 29) You are dealt a hand of three cards, one at a time. Find the probability that you have at least one queen. A) 0.068
B) 0.783
C) 0.204
D) 0.217
E) 0.213
30) The table below describes the smoking habits of a group of asthma sufferers. Light Heavy Nonsmoker smoker smoker Total Men 317 78 77 472 Women 342 64 69 475 Total 659 142 146 947 If one of the 947 subjects is randomly selected, find the probability that the person chosen is a female nonsmoker. A) 0.502 B) 0.519 C) 0.836 D) 0.361 E) 0.720
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31) So far this season, the university's football team has executed 149 running plays, 157 passing plays, and 20 "trick" plays. What is the probability that the team will execute a passing play? A) 0.518 B) 0.513 C) 0.482 D) 0.457
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32) A lot of 1000 components contains 200 that are defective. Two components are drawn at random and tested. Let A be the event that the first component drawn is defective, and let B be the event that the second component drawn is defective.
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Find P(B|A). A) 0.2
B) 0.1992
C) 0.0398
D) 0.005
33) A poll was taken of 14,972 working adults aged 40-70 to determine their level of education. The participants were classified by sex and by level of education. The results were as follows. Education Level High School or Less Bachelor's Degree Master's Degree Ph.D. Total
Male 3820 3425 508 73 7826
Female 2803 3847 442 54 7146
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Total 6623 7272 950 127 14,972
A person is selected at random. Compute the probability that the person is female and ha a bachelor's degree. A) 0.963 B) 0.538 C) 0.229 D) 0.257 34) Let A and B be events with P(A) = 0.2, P(B) = 0.5, and P(A and B) = 0.08. Are A and B independent? A) Yes B) No
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35) The letters "A", "B", "C", "D", "E", and "F" are written on six slips of paper, and the slips are placed into a hat. If the slips are drawn randomly without replacement, what is the probability that "A" is drawn first and "B" is drawn second? A) 0.039 B) 0.024 C) 0.028 D) 0.033
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Determine whether the events are disjoint, independent, neither, or both. 36) In driving a car, the events of driving over the speed limit and getting a speeding ticket A) Disjoint B) Independent C) Neither D) Both
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Answer Key Testname: CHAPTER 4 EXERCISES
1) A 2) A 3) A 4) A 5) C 6) E 7) B 8) E 9) D 10) B 11) D 12) E 13) C 14) C 15) B 16) D 17) A 18) C 19) C 20) A 21) A 22) B 23) C 24) C 25) C 26) B 27) D 28) C 29) D 30) D 31) C 32) B 33) D 34) B 35) D 36) C
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