Deck 4: Probability and Counting Rules

Question 1

Classical probability was the first type of probability studied formally by mathematicians
of the 17th and 18th centuries.

Answer 1

False

Question 2

A compound event consists of two or more outcomes or simple events.

Answer 2

False

Question 3

If one tosses a coin enough times, the number of heads and tails will tend to
"even out." This is an example of the law of .

Answer 3

large numbers

Question 4

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

Question 5

What is the set of all possible outcomes of a probability experiment?

A) the sample space
B) an outcome
C) a Venn diagram
D) events

Question 6

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

Question 7

If the probability that it will rain tomorrow is 0.39, what is the probability that it will not rain tomorrow?

A) 0.39
B) 0.61
C) -0.39
D) 1.39

Question 8

If there are 12 equally likely events, then the probability of the first one occurring is 1/

Question 9

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

Question 10

If an event cannot happen, what value is assigned to its probability?

A) 0
B) 100%
C) -1
D) 1

Question 11

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
"L" designate "locked" and U" designate "unlocked".]

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

Question 12

A child gets 20 heads out of 30 tosses of a coin. If he declared the chance of
getting a head with that coin were 2/3, that would be an example of
probability.

Question 13

The statement, "The probability that a certain sports team will win it's next game is about 60%," is an example of

A) subjective probability.
B) empirical probability.
C) a sample space.
D) classical probability.

Question 14

A probability experiment is conducted. Which of these cannot be considered a probability outcome?

Question 15

If a sportscaster makes an educated guess as to how well a team will do this season, he is using what type of probability?

A) empirical probability
B) classical probability
C) subjective probability
D) conditional probability

Question 16

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
Designate "locked" and U" designate "unlocked".]

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

Question 17

If a die were rolled, the event of getting an even number would be called a simple event.

Question 18

How many possible outcomes would there be if three coins were tossed once?

A) 2
B) 6
C) 4
D) 8

Question 19

What type of probability uses a knowledge of sample spaces as opposed to experiments to determine the numerical probability that an event will occur?

A) subjective probability
B) classical probability
C) empirical probability
D) conditional probability

Question 20

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

Question 21

For this year's mayoral election, voter dissatisfaction is very high. In a survey of 500 likely voters, 240 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) 48%
B) 24%
C) 50%
D) 52%

Question 22

According to a survey, 43% 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) 0.01
B) 0.43
C) 0.57
D) 0.75

Question 23

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

Question 24

Two events are mutually exclusive if they cannot both occur.

Question 25

A) 1/4
B) 7/12
C) 1/12
D) 2/3

Question 26

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) 1/27
C) 1/3
D) 1/6

Question 27

In a poll of 667 university students, 313 said that they were opposed to legalizing marijuana. Estimate the percentage of students who oppose legalizing marijuana.

A) 11.6%
B) 88.4%
C) 53.1%
D) 46.9%

Question 28

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

Question 29

In a poll of 416 university students, 170 said that they were opposed to legalizing marijuana. What is the probability that a surveyed student opposes legalization of
Marijuana?

A) 0.309
B) 0.691
C) 0.591
D) 0.409

Question 30

Tree diagrams are useful for

A) illustrating the law of large numbers.
B) showing that the outcome is the set of all possible sample spaces.
C) finding all possible outcomes in a probability experiment involving several steps.
D) ordering outcomes from lowest to highest.

Question 31

For this year's mayoral election, voter dissatisfaction is very high. In a survey of 100 likely voters, 26 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) 0.26
B) 0.1
C) 0.74
D) 0.026

Question 32

If a red suit is drawn from an ordinary deck of cards, what is the probability that the card is a diamond?

Question 33

Find the probability of getting a number greater than 4 when a die is rolled one time.

Question 34

If two dice are rolled one time, find the probability of getting a sum less than 5.

Question 35

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

Question 36

If two dice are rolled one time, find the probability of getting a sum of 6.

Question 37

A) 1/12
B) 1/3
C) 1/4
D) 2/3

Question 38

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

Question 39

A) 1/12
B) 2/3
C) 1/6
D) 1/4

Question 40

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

Question 41

A coin is tossed 758 times and comes up heads 409 times. Use the Empirical Method to approximate the probability that the coin comes up heads.

A) 0.35
B) 0.46
C) 0.54
D) 0.5

Question 42

wed:

A) 0.524
B) 0.476
C) 0.204
D) 0.178

Question 43

A) 0.419
B) 0.581
C) 0.5
D) 0.295

Question 44

A) 0.344
B) 0.583
C) 0.417
D) 0.239

Question 45

At a certain college, there were 700 science majors, 300 engineering majors, and business majors. If one student was selected at random, the probability that the student
Is an engineering major is

Question 46

At Wassamatta University, 59.3% of the student body are males. Choose one student at random. What is the probability that the student is female?

A) 50%
B) -9.3%
C) 40.7%
D) 59.3%

Question 47

umber is

A) 6
B) 4
C) 8
D) 16

Question 48

A Karate club consists of 41 persons holding a black belt (highest rating), 59 persons holding a brown belt (middle rating), and 73 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) 0.311
B) 0.689
C) 0.763
D) 0.237

Question 49

A Karate club consists of 52 persons holding a black belt (highest rating), 69 persons holding a brown belt (middle rating), and 83 persons holding a purple belt (lowest
Rating). What is the probability that a randomly-selected club member holds a black belt?

A) 0.745
B) 0.342
C) 0.658
D) 0.255

Question 50

A) 0.618
B) 0.33
C) 0.382
D) 0.659

Question 51

A probability experiment has two steps. There are two possible results for the first step, call them "A" and "B". If the result for the first step was "A", then there would be 5
Possible results for the second step. If the result for the first step was "B", then there
Would be 12 possible results for the second step. How many possible outcomes are there
For this experiment?

A) 60
B) 17
C) 8
D) 12

Question 52

wed:

A) 0.762
B) 0.808
C) 0.192
D) 0.238

Question 53

So far this season, the university's football team has executed 145 running plays, 149 passing plays, and 24 "trick" plays. What is the probability that the team will execute a
Passing play?

A) 0.469
B) 0.507
C) 0.531
D) 0.456

Question 54

wed:

A) 0.777
B) 0.025
C) 0.198
D) 0.223

Question 55

cycling

Question 56

The staff at a small company includes: 4 secretaries, 20 technicians, 4 engineers, 2 executives, and 50 factory workers. If a person is selected at random, what is the
Probability that he or she is a factory worker?

Question 57

n

A) 0.235
B) 0.00018
C) 0.0154
D) 0.0153

Question 58

A) 0.951
B) 0.047
C) 0.049
D) 0.953

Question 59

So far this season, the university's football team has executed 155 running plays, 143 passing plays, and 19 "trick" plays. What is the probability that the team will not execute
A trick play?

A) 0.06
B) 0.064
C) 0.94
D) 0.936

Question 60

Question 61

f the

A) 0.1579
B) 0.5833
C) 0.5526
D) 0.3947

Question 62

Out of 733 items checked out of a public library, 269 were fiction books, 222 were non-fiction books, and 242 were videos (of any genre). What is the probability that a
Randomly-selected item was not a video?

A) 0.367
B) 0.493
C) 0.67
D) 0.33

Question 63

If a single card is drawn from an ordinary deck of cards, what is the probability of drawing a jack, queen, king, or ace?

Question 64

Question 65

A) 0.27
B) 0.53
C) 0.6
D) 0.13

Question 66

In a fish tank, there are 15 goldfish, 6 angelfish, and 18 guppies. If a fish is selected at random, find the probability that it is an angelfish or a guppy.

Question 67

A single card is drawn from a deck. Find the probability of selecting a heart or a 8.

Question 68

Two dice are rolled. Find the probability of getting doubles or a sum of 2.

Question 69

A) 0.79
B) 0.822
C) 0.91
D) 0.21

Question 70

On a recent Saturday, a total of 1112 people visited a local library. Of these people, 266 were under age 10, 496 were aged 10-18, 189 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) 0.446
B) 0.239
C) 0.685
D) 0.762

Question 71

A) 0.106
B) 0.139
C) 0.033
D) 0.073

Question 72

In a recent semester at a local university, 500 students enrolled in both General Chemistry and Calculus I. Of these students, 66 received an A in general chemistry, 73
Received an A in calculus, and 33 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) 0.278
B) 0.344
C) 0.763
D) 0.212

Question 73

A) 0.811
B) 0.159
C) 0.189
D) 0.22

Question 74

In a recent semester at a local university, 490 students enrolled in both General Chemistry and Calculus I. Of these students, 83 received an A in general chemistry, 86
Received an A in calculus, and 33 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) 0.831
B) 0.763
C) 0.169
D) 0.824

Question 75

A) 0.186
B) 0.149
C) 0.107
D) 0.091

Question 76

If one card is drawn from an ordinary deck of cards, what is the probability that the card will be an ace, a king of hearts, or a spade?

Question 77

A) 0.3
B) 0.71
C) 0.61
D) 0.9

Question 78

Question 79

On a recent Saturday, a total of 1086 people visited a local library. Of these people, 269 were under age 10, 466 were aged 10-18, 185 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) 0.735
B) 0.153
C) 0.677
D) 0.323

Question 80

A) 0.528
B) 0.998
C) 0.256
D) 0.257