Deck 5: Probability

Question 1

A Karate club consists of 52 persons holding a black belt (highest rating), 69 persons holding a brown belt (middle rating), and 77 persons holding a purple belt (lowest rating). What is the
Probability that a randomly-selected club member holds a brown belt or a purple belt?

A) 0.644
B) 0.737
C) 0.356
D) 0.263

Answer 1

0.737

Question 2

A 12 -sided die can be made from a geometric solid called a dodecahedron. Assume that a fair dodecahedron is rolled.
The sample space is {1,2,3,4,5,6,7,8,9,10,11,12}.
Find P (Less than 4).

A) 7 / 12
B) 1 / 4
C) 1 / 12
D) 1 / 3

Answer 2

1 / 4

Question 3

In a poll of 628 university students, 276 said that they were opposed to legalizing marijuana. What is the probability that a surveyed student opposes legalization of marijuana?

A) 0.216
B) 0.439
C) 0.784
D) 0.561

Answer 3

0.439

Question 4

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) 7 / 9
B) 5 / 9
C) 1 / 3
D) 2 / 3

Question 5

For this year's mayoral election, voter dissatisfaction is very high. In a survey of 500 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) 0.5
B) 0.58
C) 0.21
D) 0.42

Question 6

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 the second answer is either "B" or "C". [Hint: List all the outcomes of the sample
Space first.]

A) 7 / 9
B) 1 / 3
C) 2 / 3
D) 5 / 9

Question 7

In a poll of 420 university students, 197 said that they were opposed to legalizing marijuana. Estimate the percentage of students who oppose legalizing marijuana.

A) 11.7%
B) 53.1%
C) 88.3%
D) 46.9%

Question 8

So far this season, the university's football team has executed 146 running plays, 167 passing plays, and 22 "trick" plays. What is the probability that the team will execute a passing play?

A) 0.436
B) 0.534
C) 0.501
D) 0.499

Question 9

The arrow on the spinner shown below can be spun so that the arrowhead eventually stops in one of the three sectors labeled "A", "B", or "C". The spinner is spun 109 times and comes up "A" 56
Times. Use the Empirical Rule to approximate the probability that the spinner comes up "A".

A) 0.5
B) 0.514
C) 0.486
D) 0.339

Question 10

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 both answers are the same ("AA", "BB" or "CC"). [Hint: List all the outcomes of the
Sample space first.]

A) 1 / 27
B) 1 / 6
C) 1 / 9
D) 1 / 3

Question 11

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 both answers are "C". [Hint: List all the outcomes of the sample space first.]

A) 1 / 9
B) 1 / 6
C) 1 / 3
D) 1 / 27

Question 12

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

A)
B)
C)
D)

Question 13

A 12 -sided die can be made from a geometric solid called a dodecahedron. Assume that a fair dodecahedron is rolled.
The sample space is {1,2,3,4,5,6,7,8,9,10,11,12}.
Find P(10).

A) 1 / 12
B) 5 / 6
C) 1 / 6
D) 3 / 4

Question 14

So far this season, the university's football team has executed 151 running plays, 152 passing plays, and 18 "trick" plays. What is the probability that the team will not execute a trick play?

A) 0.059
B) 0.941
C) 0.056
D) 0.944

Question 15

For this year's mayoral election, voter dissatisfaction is very high. In a survey of 700 likely voters, 182 said they planned to write in an independent candidate rather than vote for the Democrat or Republican
Candidate for mayor.
Estimate the percentage of voters who plan to write in an independent candidate?

A) 70%
B) 18.2%
C) 26%
D) 74%

Question 16

According to a survey, 45% of teenagers could recognize a picture of legendary film star John Wayne. What is the probability that a randomly-selected teenager could recognize John Wayne?

A) 0.55
B) 0.45
C) 0.01
D) 0.82

Question 17

A coin is tossed 764 times and comes up heads 397 times. Use the Empirical Method to approximate the probability that the coin comes up heads.

A) 0.52
B) 0.5
C) 0.342
D) 0.48

Question 18

A 12 -sided die can be made from a geometric solid called a dodecahedron. Assume that a fair dodecahedron is rolled.
The sample space is {1,2,3,4,5,6,7,8,9,10,11,12}.
Find P( Greater than 8).

A) 1 / 12
B) 1 / 3
C) 1 / 4
D) 7 / 12

Question 19

A Karate club consists of 54 persons holding a black belt (highest rating), 64 persons holding a brown belt (middle rating), and 79 persons holding a purple belt (lowest rating). What is the
Probability that a randomly-selected club member holds a black belt?

A) 0.378
B) 0.622
C) 0.726
D) 0.274

Question 20

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 neither of the answers is "B".
[Hint: List all the outcomes of the sample space first.]

A) 4 / 9
B) 2 / 3
C) 5 / 9
D) 1 / 3

Question 21

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 22

If P(A)=0.69, P(B)=0.4, and P(A or B)=0.73, are A and B mutually exclusive?

A) No
B) Yes

Question 23

A survey asked 31,156 homeowners how many pets they owned. The results were as follows: What is the probability that a sampled homeowner has more than 1 pet?

A) 0.208
B) 0.525
C) 0.215
D) 0.475

Question 24

If P(A^C)=0.41, find P(A)

A) 0.205
B) 0.59
C) 0.41
D) 0.295

Question 25

There are 30,136 undergraduate students enrolled at a certain university. The age distribution is as follows: What is the probability that a student is between 23 and 30 years old?

A) 0.368
B) 0.415
C) 0.217
D) 0.585

Question 26

If P(A)=0.43, P(B)=0.21, and P(A or B)=0.64, are A and B mutually exclusive?

A) Yes
B) No

Question 27

A survey asked respondents to indicate their level of satisfaction with government spending. The results are show below. What is the probability that a sampled person was only somewhat satisfied or dissatisfied with government's
Spending?

A) 0.897
B) 0.094
C) 0.906
D) 0.103

Question 28

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

A)
B)
C)
D) None of these.

Question 29

For the event described below, which of the following represents the complement of the event? A sample of 357 software DVDs was selected. Fewer than 44 of these were defective.

A) Fewer than 44 DVDs were not defective.
B) At least 44 DVDs were defective.
C) More than 44 DVDs were not defective.
D) At most 44 DVDs were not defective.

Question 30

A survey asked 33,691 homeowners how many pets they owned. The results were as follows: What is the probability that a sampled homeowner has three pets?

A) 0.774
B) 0.019
C) 0.207
D) 0.226

Question 31

A survey asked respondents to indicate their level of satisfaction with government spending. The results are show below. 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) 0.407
B) 0.593
C) 0.633
D) 0.33

Question 32

There are 29,091 undergraduate students enrolled at a certain university. The age distribution is as follows: What is the probability that a student is less than 18 years old?

A) 0.0073
B) 0.0071
C) 0.00014
D) 0.236

Question 33

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 34

For the event described below, which of the following represents the complement of the event? A sample of 491 software DVDs was selected. Exactly 42 of these were defective.

A) Exactly 449 DVDs were not defective.
B) No more than 42 DVDs were defective.
C) The number of defective DVDs was not equal to 42.
D) Exactly 42 DVDs were not defective.

Question 35

A survey asked 33,625 homeowners how many pets they owned. The results were as follows: 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) 0.833
B) 0.201
C) 0.799
D) 0.167

Question 36

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 37

For the event described below, which of the following represents the complement of the event? A sample of 442 software DVDs was selected. At least 29 of these were defective.

A) Fewer than 29 DVDs were defective.
B) Exactly 29 DVDs were not defective.
C) At most 29 DVDs were defective.
D) At most 413 DVDs were not defective.

Question 38

If P(A)=0.54, P(B)=0.57, and P(A and B)=0.29, find P(A or B)

A) 0.29
B) 0.82
C) 0.145
D) 0.555

Question 39

If P(A)=0.33, find P(A^C).

A) 0.33
B) 0.335
C) 0.67
D) 0.165

Question 40

If P(A)=0.57, P(B)=0.35, and A and B are mutually exclusive, find P(A or B).

A) 0.46
B) 0.22
C) 0
D) 0.92

Question 41

On a recent Saturday, a total of 1,087 people visited a local library. Of these people, 249 were under age 10, 479 were aged 10-18, 180 were aged 19-30, and the rest were more than 30 years old.
One person is sampled at random. What is the probability that the person is less than 19 years old?

A) 0.441
B) 0.67
C) 0.728
D) 0.229

Question 42

Nanette must pass through three doors as she walks from her company's foyer to her office. Each of 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) {LLU, LUL, ULL, LUU, ULU, UUL}
B) {UUU, LUU, ULU, UUL}
C) {LLL, LLU, LUL, LUU, ULL, ULU, UUL, UUU}
D) None of these.

Question 43

There are 25 students in a sixth-grade class. On a cold winter day in February, many of the students had runny noses and sore throats. After examining each student, the school nurse constructed the following table: Find the probability that a randomly-selected student has neither a runny nose nor a sore throat.

A) 0.48
B) 0.32
C) 0.20
D) 0.80

Question 44

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

A)
B)
C)
D) None of these.

Question 45

Nanette must pass through three doors as she walks from her company's foyer to her office. Each of these doors may be locked or unlocked. Let C be the event that at least two doors are in the same condition. List the outcomes of 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

Out of 920 items checked out of a public library, 397 were fiction books, 285 were non-fiction books, and 238 were videos (of any genre). What is the probability that a randomly-selected item
Was not a video?

A) 0.349
B) 0.432
C) 0.741
D) 0.259

Question 47

On a certain day, a cheese packaging facility packaged 500 units of mozzarella cheese. Some of these packages had major flaws, some had minor flaws, and some had both major andminor flaws.
The following table presents the results. Find the probability that randomly chosen cheese package has a minor flaw.

A) 0.104
B) 0.237
C) 0.178
D) 0.146

Question 48

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. Suppose that P(E)=0.24, P(B)=0.17, and P(E and B)=0.1 . Find the probability that a corn crop ha either an ear worm infestation, a corn borer infestation, or both.

A) 0.51
B) 0.1
C) 0.31
D) 0.59

Question 49

There are 25 students in a sixth-grade class. On a cold winter day in February, many of the students had runny noses and sore throats. After examining each student, the school nurse constructed the following table: Find the probability that a randomly-selected student has a runny nose.

A) 0.64
B) 0.36
C) 0.20
D) 1.25

Question 50

On a certain day, a cheese packaging facility packaged 480 units of mozzarella cheese. Some of these packages had major flaws, some had minor flaws, and some had both major and
Minor flaws. The following table presents the results. Find the probability that randomly chosen cheese package has no major flaw.

A) 0.2
B) 0.8
C) 0.91
D) 0.831

Question 51

On a certain day, a cheese packaging facility packaged 560 units of mozzarella cheese. Some of these packages had major flaws, some had minor flaws, and some had both major and minor
Flaws. The following table presents the results. Find the probability that randomly chosen cheese package has a major flaw.

A) 0.073
B) 0.045
C) 0.029
D) 0.088

Question 52

On a certain day, a cheese packaging facility packaged 500 units of mozzarella cheese. Some of these packages had major flaws, some had minor flaws, and some had both major and
Minor flaws. The following table presents the results. Find the probability that randomly chosen cheese package has a flaw (major or minor).

A) 0.264
B) 0.168
C) 0.784
D) 0.216

Question 53

In a recent semester at a local university, 490 students enrolled in both General Chemistry and Calculus I. Of these students, 66 received an A in general chemistry, 58 received an A in calculus,
And 30 received an A in both general chemistry and calculus.
Find the probability that a randomly chosen student received an A in general chemistry or calculus or both.

A) 0.758
B) 0.314
C) 0.192
D) 0.253

Question 54

A poll was taken of 14,537 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. A person is selected at random. Compute the probability that the person is female and has a bachelor's degree.

A) 0.978
B) 0.520
C) 0.243
D) 0.266

Question 55

Nanette must pass through three doors as she walks from her company's foyer to her office. Each of these doors may be locked or unlocked. Let B be the event that exactly two doors are in the same condition. 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}
C) {LLU, LUL, ULL, LUU, ULU, UUL}
D) None of these.

Question 56

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. Suppose that P(E)=0.27, P(B)=0.11, and P(E and B)=0.1 . Find the probability that a corn crop ha no corn borer infestation.

A) 0.73
B) 0.62
C) 0.28
D) 0.89

Question 57

Nanette must pass through three doors as she walks from her company's foyer to her office. Each of 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) {LLU, LUL, ULL}}
B) {LLL, LLU, LUL, LUU, ULL, ULU, UUL, UUU}
C) {LLU, LUL, ULL, LUU, ULU, UUL}
D) None of these.

Question 58

In a recent semester at a local university, 540 students enrolled in both General Chemistry and Calculus I. Of these students, 51 received an A in general chemistry, 59 received an A in calculus,
And 30 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) 0.906
B) 0.094
C) 0.891
D) 0.85

Question 59

On a recent Saturday, a total of 1,049 people visited a local library. Of these people, 245 were under age 10, 464 were aged 10-18, 181 were aged 19-30, and the rest were more than 30 years old.
One person is sampled at random. What is the probability that the person is more than 30 years old?

A) 0.324
B) 0.676
C) 0.152
D) 0.709

Question 60

There are 25 students in a sixth-grade class. On a cold winter day in February, many of the students had runny noses and sore throats. After examining each student, the school nurse constructed the following table: Find the probability that a randomly-selected student has a sore throat.

A) 0.36
B) 0.24
C) 0.20
D) 0.50

Question 61

A geneticist is studying two genes. Each gene can be either dominant or recessive. A sample of 100 individuals is categorized as follows. What is the probability that in a randomly-sampled individual, gene 1 is dominant?

A) 0.10
B) 0.04
C) 0.90
D) 0.40

Question 62

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 colonel.
B: The soldier is a lieutenant.

A) neither
B) independent
C) mutually exclusive

Question 63

Let A and B be events with

A) 0.08
B) 0.25
C) 0.32
D) 0.16

Question 64

A fair die is rolled five times. What is the probability that it comes up 1 at least once?

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

Question 65

The lette 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 "E" is
Drawn first and "F" is drawn second?

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

Question 66

Let A and B be events with P(A)=0.4, P(B)=0.8 . Assume that A and B are independent. Find P(A and B)

A) 0.32
B) 0.5
C) 0.4
D) 0.8

Question 67

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

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

Question 68

A poll was taken of 13,795 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. A person is selected at random. Compute the probability that the person has a master's degree.

A) 0.032
B) 0.036
C) 0.073
D) 0.041

Question 69

A fast-food restaurant chain has 628 outlets in the United States. The following table categorizes them by city population and location and presents the number of outlets in each category. An outlet
Is chosen at random from the 628 to test market a new menu. 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) 0.174
B) 0.321
C) 0.053
D) 0.303

Question 70

A geneticist is studying two genes. Each gene can be either dominant or recessive. A sample of 100 individuals is categorized as follows. What is the probability that in a randomly-sampled individual, gene 2 is dominant?

A) 0.70
B) 0.12
C) 0.40
D) 0.60

Question 71

Let A and B be events with . Are A and B mutually exclusive?

A) No
B) Yes

Question 72

Let A, B and C be independent events with P(A) = 0.4, P(B) = 0.1, and P(C) = 0.3. Find P(A and B andC)

A) 0.133
B) 0.04
C) 0.012
D) 0.015

Question 73

Let A and B be events with independent?

A) Yes
B) No

Question 74

A geneticist is studying two genes. Each gene can be either dominant or recessive. A sample of 100 individuals is categorized as follows. Two genes are said to be in linkage equilibrium if the event that gene 1 is dominant is independent of the event
That gene 2 is dominant. Are these genes in linkage equilibrium?

A) No
B) Yes

Question 75

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

A) 0.25
B) 0.9744
C) 0.8704
D) 0.936

Question 76

A geneticist is studying two genes. Each gene can be either dominant or recessive. A sample of 100 individuals is categorized as follows. Given that gene 1 is dominant, what is the probability that gene 2 is dominant?

A) 0.35
B) 0.39
C) 0.40
D) 2.50

Question 77

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

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

Question 78

Let A and B be events with independent?

A) No
B) Yes

Question 79

A fast-food restaurant chain has 622 outlets in the United States. The following table categorizes them by city population and location and presents the number of outlets in each category. An outlet
Is chosen at random from the 622 to test market a new menu. 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) 0.327
B) 0.703
C) 0.238
D) 0.138

Question 80

A poll was taken of 14,360 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. A person is selected at random. Compute the probability that the person is male or has a Ph.D.

A) 0.518
B) 0.007
C) 0.514
D) 0.511