Deck 5: Discrete Probability Distributions

Question 1

A section of an exam contains two multiple-choice questions, each with three answerchoices (listed "A", "B", and "C"). List all the outcomes of the sample space.

A){AB, AC, BA, BC, CA, CB}
B){AA, AB, AC, BB, BC, CC}
C){AA, AB, AC, BA, BB, BC, CA, CB, CC}
D){A, B, C}

Answer 1

C

Question 2

A Karate club consists of 35 persons holding a black belt (highest rating), 64 personsholding a brown belt (middle rating), and 97 persons holding a purple belt (lowestrating). What is the probability that a randomly-selected club member holds a black belt?

A)0.821
B)0.179
C)0.783
D)0.217

Answer 2

B

Question 3

A coin is tossed 475 times and comes up heads 242 times. Use the Empirical Method toapproximate the probability that the coin comes up heads.

A)0.338
B)0.509
C)0.5
D)0.491

Answer 3

B

Question 4

A 12-sided die can be made from a geometric solid called adodecahedron. )

Question 5

A section of an exam contains two multiple-choice questions, each with three answerchoices (listed "A", "B", and "C"). Assuming the outcomes to be equally likely, find theprobability (as a reduced fraction)that both answers are "C". [Hint: List all the outcomesof the sample space first.]

Question 6

A section of an exam contains two multiple-choice questions,)

Question 7

A 12-sided die can be made from a geometric solid called adodecahedron. )

Question 8

A Karate club consists of 46 persons holding a black belt (highest rating), 52 personsholding a brown belt (middle rating), and 95 persons holding a purple belt (lowestrating). What is the probability that a randomly-selected club member holds a brown beltor a purple belt?

A)0.313
B)0.762
C)0.238
D)0.687

Question 9

For this year's mayoral election, voter dissatisfaction is very high. In a survey of 500likely voters, 210 said they planned to write in an independent candidate rather than vote for theDemocrat or Republican candidate for mayor.What is the probability that a surveyed voter plans to write in an independent candidate?

A)0.42
B)0.58
C)0.5
D)0.21

Question 10

In a poll of 451 university students, 193 said that they were opposed to legalizingmarijuana. What is the probability that a surveyed student opposes legalization ofmarijuana?

A)0.428
B)0.748
C)0.572
D)0.252

Question 11

So far this season, the university's football team has executed 163 running plays, 138passing plays, and 24 "trick" plays. What is the probability that the team will not executea trick play?

A)0.08
B)0.074
C)0.926
D)0.92

Question 12

A section of an exam contains two multiple-choice questions,)

Question 13

According to a survey, 68% of teenagers could recognize a picture of legendary film starJohn Wayne. What is the probability that a randomly-selected teenager could recognizeJohn Wayne?

A)0.01
B)0.47
C)0.68
D)0.32

Question 14

The arrow on the spinner shown below can be spun so that the arrowhead eventually

Question 15

A section of an exam contains two multiple-choice questions,)

Question 16

So far this season, the university's football team has executed 149 running plays, 157passing plays, and 20 "trick" plays. What is the probability that the team will execute apassing play?

A)0.513
B)0.457
C)0.482
D)0.518

Question 17

In a poll of 724 university students, 311 said that they were opposed to legalizingmarijuana. Estimate the percentage of students who oppose legalizing marijuana.

A)75.3%
B)24.7%
C)43%
D)57%

Question 18

A section of an exam contains two multiple-choice questions,)

Question 19

A survey asked respondents to indicate their level of satisfaction with government What is the probability that a sampled person was only somewhat satisfied or dissatisfied with
Government's spending?

A)0.067
B)0.072
C)0.928
D)0.933

Question 20

For this year's mayoral election, voter dissatisfaction is very high. In a survey of 800likely voters, 231 said they planned to write in an independent candidate rather than vote for theDemocrat or Republican candidate for mayor.Estimate the percentage of voters who plan to write in an independent candidate?

A)28.875%
B)71.125%
C)80%
D)23.1%

Question 21

A survey asked 33,347 homeowners how many pets they owned. The results were as followed: Assume this is a simple random sample of homeowners. Use the Empirical Method to
Estimate the probability that a homeowner has at least one pet.

A)0.837
B)0.195
C)0.163
D)0.805

Question 22

For the event described below, which of the following represents the complement of the event.A sample of 301 software DVDs was selected. At least 34 of these were defective.

A)Fewer than 34 DVDs were defective.
B)Exactly 34 DVDs were not defective.
C)At most 34 DVDs were defective.
D)At most 267 DVDs were not defective.

Question 23

Nanette must pass through three doors as she walks from her company's foyer to her office. Eachof these doors may be locked or unlocked.Let A be the event that all three doors are in the same condition. List the outcomes ofA. [Let "L" designate "locked" and U" designate "unlocked".]

A){LLL, LLU, LUL, LUU, ULL, ULU, UUL, UUU}
B){LLL}
C){LLL, UUU}
D)None of these.

Question 24

If P(A)=0.4, P(B)=0.36 , and P(A or B)=0.76 , are A and B mutually exclusive?

A) Yes
B) No

Question 25

If P(A)=0.76, P(B)=0.4 , and P(A and B)=0.27 , find P(A or B) .

A) 0.89
B) 0.135
C) 0.58
D) 0.27

Question 26

A survey asked respondents to indicate their level of satisfaction with government Assume this is a simple random sample from a population. Use the Empirical Method to estimate the probability that a person is dissatisfied with government's spending?

A)0.609
B)0.391
C)0.33
D)0.647

Question 27

Nanette must pass through three doors as she walks from her company's foyer to her office. Eachof these doors may be locked or unlocked.List the outcomes of the sample space.

A){LLU, LUL, ULL, UUL, ULL, LUU}
B){LLL, UUU}
C){LLL, LLU, LUL, LUU, ULL, ULU, UUL, UUU}
D)None of these.

Question 28

A survey asked 33,703 homeowners how many pets they owned. The results were as followed: What is the probability that a sampled homeowner has three pets?

A)0.78
B)0.192
C)0.028
D)0.22

Question 29

If find P(A) .

A) 0.39
B) 0.195
C) 0.305
D) 0.61

Question 30

If P(A)=0.79 , find

A) 0.79
B) 0.21
C) 0.395
D) 0.105

Question 31

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.

A)A and B are mutually exclusive.
B)A and B are complementary.
C)A and B are not mutually exclusive.
D)If B is true, A is true.

Question 32

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 437 DVDs were not defective.
B)The number of defective DVDs was not equal to 34.
C)No more than 34 DVDs were defective.
D)Exactly 34 DVDs were not defective.

Question 33

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.
B)B is the complement of A.
C)A and B are not mutually exclusive.
D)If B is not true, A cannot be true.

Question 34

A survey asked 33,083 homeowners how many pets they owned. The results were as followed: What is the probability that a sampled homeowner has more than 1 pet?

A)0.505
B)0.495
C)0.166
D)0.176

Question 35

For the event described below, which of the following represents the complement of the event.A sample of 372 software DVDs was selected. Fewer than 41 of these weredefective.

A)More than 41 DVDs were not defective.
B)At most 41 DVDs were not defective.
C)At least 41 DVDs were defective.
D)Fewer than 41 DVDs were not defective.

Question 36

There are 29,735 undergraduate students enrolled at a certain university. ) What is the probability that a student is less than 18 years old?

A)0.0096
B)0.0094
C)0.218
D)0.00017

Question 37

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.

A)A and B are mutually exclusive.
B)A and B are complementary.
C)A and B are not mutually exclusive.
D)If B is untrue, A is untrue.

Question 38

There are 27,307 undergraduate students enrolled at a certain university. ) What is the probability that a student is between 23 and 30 years old?

A)0.347
B)0.579
C)0.421
D)0.232

Question 39

If P(A)=0.33, P(B)=0.51 , and A and B are mutually exclusive, find P(A or B) .

A) 0.84
B) 0
C) 0.42
D) 0.18

Question 40

If P(A)=0.46, P(B)=0.37 , and P(A or B)=0.61 , are A and B mutually exclusive?

A) No
B) Yes

Question 41

Nanette must pass through three doors as she walks from her company's foyer to her office. Eachof these doors may be locked or unlocked.Let B be the event that exactly two doors are locked. List the outcomes of B. [Let "L"designate "locked" and U" designate "unlocked".]

A){LLL, LLU, LUL, LUU, ULL, ULU, UUL, UUU}
B){LLU, LUL, ULL, LUU, ULU, UUL}
C){LLU, LUL, ULL}
D)None of these.

Question 42

In a recent semester at a local university, 520 students enrolled in both GeneralChemistry and Calculus I. Of these students, 88 received an A in general chemistry, 76received an A in calculus, and 31 received an A in both general chemistry and calculus.Find the probability that a randomly chosen student received an A in general chemistry or calculusor both.

A)0.811
B)0.375
C)0.256
D)0.315

Question 43

Let A and B be events with P(A)=0.7, P(B)=0.5 , and P(B / A)=0.4 . Find P(A and B) .

A) 0.57
B) 0.2
C) 0.28
D) 0.35

Question 44

Out of 829 items checked out of a public library, 282 were fiction books, 294 werenon-fiction books, and 253 were videos (of any genre). What is the probability that arandomly-selected item was not a video?

A)0.439
B)0.340
C)0.305
D)0.695

Question 45

Nanette must pass through three doors as she walks from her company's foyer to her office. Eachof these doors may be locked or unlocked.Let C be the event that at least two doors are in the same condition. List the outcomesof C. [Let "L" designate "locked" and U" designate "unlocked".]

A){LLL, UUU, LLU, LUL, ULL}
B){LLU, LUL, ULL, LUU, ULU, UUL}
C){LLL, LLU, LUL, LUU, ULL, ULU, UUL, UUU}
D)None of these.

Question 46

Nanette must pass through three doors as she walks from her company's foyer to her office. Eachof these doors may be locked or unlocked.Let B be the event that exactly two doors are in the same condition. List the outcomesof B. [Let "L" designate "locked" and U" designate "unlocked".]

A){LLL, LLU, LUL, LUU, ULL, ULU, UUL, UUU}
B){LLU, LUL, ULL}
C){LLU, LUL, ULL, LUU, ULU, UUL}
D)None of these.

Question 47

On a recent Saturday, a total of 1100 people visited a local library. Of these people, 260were under age 10, 496 were aged 10-18, 180 were aged 19-30, and the rest were more than30 years old.One person is sampled at random. What is the probability that the person is less than 19 years old?

A)0.451
B)0.687
C)0.756
D)0.236

Question 48

Nanette must pass through three doors as she walks from her company's foyer to her office. Eachof these doors may be locked or unlocked.Let C be the event that at least two doors are unlocked. List the outcomes of C. [Let"L" designate "locked" and U" designate "unlocked".]

A){UUU, LUU, ULU, UUL}
B){LLL, LLU, LUL, LUU, ULL, ULU, UUL, UUU}
C){LLU, LUL, ULL, LUU, ULU, UUL}
D)None of these.

Question 49

Let E be the event that a corn crop has an infestation of ear worms,)

Question 50

A poll was taken of 14,972 working adults aged 40-70 to determine their level of education. A person is selected at random. Compute the probability that the person is female and has a
Bachelor's degree.

A)0.229
B)0.538
C)0.963
D)0.257

Question 51

On a certain day,) Find the probability that randomly chosen cheese package has no major flaw.

A)0.89
B)0.217
C)0.835
D)0.783

Question 52

In a recent semester at a local university, 540 students enrolled in both GeneralChemistry and Calculus I. Of these students, 72 received an A in general chemistry, 65received an A in calculus, and 31 received an A in both general chemistry and calculus.Find the probability that a randomly chosen student did not receive an A in general chemistry.

A)0.88
B)0.867
C)0.133
D)0.809

Question 53

On a certain day,) Find the probability that randomly chosen cheese package has a minor flaw.

A)0.172
B)0.138
C)0.095
D)0.105

Question 54

On a certain day,) Find the probability that randomly chosen cheese package has a flaw (major or minor).

A)0.779
B)0.254
C)0.188
D)0.221

Question 55

A poll was taken of 14,056 working adults aged 40-70 to determine their level of education. A person is selected at random. Compute the probability that the person has a master's degree.

A)0.036
B)0.034
C)0.072
D)0.038

Question 56

On a certain day,) Find the probability that randomly chosen cheese package has a major flaw.

A)0.16
B)0.048
C)0.124
D)0.076

Question 57

Let A and B be events with P(A)=0.8, P(B)=0.6 . Assume that A and B are independent. Find P(A and B) .

A) 0.8
B) 0.6
C) 0.48
D) 0.75

Question 58

Let E be the event that a corn crop has an infestation of ear worms,)

Question 59

A poll was taken of 14,292 working adults aged 40-70 to determine their level of education. A person is selected at random. Compute the probability that the person is male or has a Ph.D.

A)0.523
B)0.525
C)0.008
D)0.530

Question 60

On a recent Saturday, a total of 1062 people visited a local library. Of these people, 233were under age 10, 493 were aged 10-18, 168 were aged 19-30, and the rest were more than30 years old.One person is sampled at random. What is the probability that the person is more than 30 yearsold?

A)0.316
B)0.684
C)0.158
D)0.726

Question 61

A fair coin is tossed four times. What is the probability that the sequence of tosses isHHTT?

A)0.038
B)0.125
C)0.0625
D)0.25

Question 62

At the campus cafeteria, a diner can purchase a "meal deal" that consists of an entree, aside dish, and a dessert. There are 3 choices for the entree, 5 choices for the side dish,and 3 choices for dessert. How many different meal deals are possible?

A)39
B)165
C)45
D)11

Question 63

On a TV game show, a contestant is shown 9 products from a grocery store and is askedto choose the three least-expensive items in the set. The three chosen items need not bein any particular order. In how many ways can the contestant choose the three items?

A)6
B)504
C)60,480
D)84

Question 64

A fair die is rolled two times. What is the probability that both rolls are 3?

A)0.167
B)0.028
C)0.0046
D)0.083

Question 65

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

Question 66

An unfair coin has a probability 0.4 of landing heads. The coin is tossed two times. Whatis the probability that it lands heads at least once?

A)0.64
B)0.5
C)0.84
D)0.6

Question 67

Evaluate the combination:

A) 210
B) 5040
C) 35
D) 21

Question 68

A fast-food restaurant chain has 617 outlets in the United States. ) Given that the outlet is located in the West (either SW or NW), what is the probability that it is in a city with population 50,000-500,000?

A)0.156
B)0.268
C)0.716
D)0.368

Question 69

Evaluate the factorial:

A) 100
B) 3,628,800
C) 90
D) 362,880

Question 70

A fast-food restaurant chain has 623 outlets in the United States. ) Given that the outlet is located in a city with a population under 50,000, what is the probability that it is in the Southwest?

A)0.164
B)0.255
C)0.265
D)0.043

Question 71

Assume a soldier is selected at random from the Army. Determine whether the events Aand B are independent, mutually exclusive, or neither.A: The soldier is a corporal.B: The soldier is a colonel.

A)mutually exclusive
B)neither
C)independent

Question 72

A fair die is rolled five times. What is the probability that it comes up 5 at least once?

A)0.1667
B)0.5981
C)0.5177
D)0.8333

Question 73

Let A and B be events with P(A)=0.9, P(B)=0.5 , and P(A and B)=0.45 . Are A and B independent?

A) Yes
B) No

Question 74

A lot of 1000 components contains 300 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.
Find P(B and A) .

A) 0.0033
B) 0.3
C) 0.0898
D) 0.2993

Question 75

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

Question 76

The letters "A", "B", "C", "D", "E", and "F" are written on six slips of paper, and theslips are placed into a hat. If the slips are drawn randomly without replacement, what isthe probability that "A" is drawn first and "B" is drawn second?

A)0.028
B)0.039
C)0.033
D)0.024

Question 77

A lot of 1000 components contains 150 that are defective. Two components are drawn atrandom and tested. Let A be the event that the first component drawn is defective, and letB be the event that the second component drawn is defective.Find P(A).

A)0.0224
B)0.1491
C)0.15
D)0.0067

Question 78

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.
Find

A) 0.0398
B) 0.2
C) 0.1992
D) 0.005

Question 79

62)

Question 80

Evaluate the permutation:

A) 5040
B) 40
C) 210
D) 3,628,800