Deck 3: Probability

Question 1

A bag of candy was opened and the number of pieces was counted. The results are shown in the table below: Find the probability that a randomly chosen piece of candy is not blue or red.

A)0.60
B)0.40
C)0.15
D)0.85

Answer 1

0.60

Question 2

Which of the following assignments of probabilities to the sample points A, B, and C is valid if A, B, and C are the only sample points in the experiment?

A)
B)
C)
D)

Answer 2

Question 3

Which number could be the probability of an event that is almost certain to occur?

A).99
B).01
C)1.01
D).51

Answer 3

.99

Question 4

A bag of colored candies contains 20 red, 25 yellow, and 35 orange candies. An experiment consists of randomly choosing one candy from the bag and recording its color. What is the sample space for
This experiment?

A) {20,25,35}
B) {80}
C)
D)

Question 5

The outcome of an experiment is the number of resulting heads when a nickel and a dime are flipped simultaneously. What is the sample space for this experiment?

A) {nickel, dime}
B) {{HH}, {HT}, {TH}, {TT}}
C) {0,1,2}
D) {{HH}, {HT}, {TT}}

Question 6

Fill in the blank. A(n)______ is a process that leads to a single outcome that cannot be predicted with certainty.

A)experiment
B)event
C)sample space
D)sample point

Question 7

A bag of candy was opened and the number of pieces was counted. The results are shown in the table below: List the sample space for this problem.

A){25, 20, 20, 15, 10, 10}
B){0.25, 0.20, 0.20, 0.15, 0.10, 0.10}
C){Red}
D){Red, Brown, Green, Blue, Yellow, Orange}

Question 8

A statistical experiment can be almost any act of observation as long as the outcome is uncertain.

Question 9

In any experiment with exactly four sample points in the sample space, the probability of each
sample point is .25.

Question 10

An experiment consists of randomly choosing a number between 1 and 10. Let E be the event that the number chosen is even. List the sample points in E.

A)
B)
C)
D)

Question 11

Fill in the blank. A(n)__________ is the most basic outcome of an experiment.

A)experiment
B)sample point
C)event
D)sample space

Question 12

Fill in the blank. The __________ is the collection of all the sample points in an experiment.

A)sample space
B)event
C)Venn diagram
D)union

Question 13

Suppose that an experiment has five equally likely outcomes. What probability is assigned to each of the sample points?

A)1
B).5
C).05
D).2

Question 14

If sample points A, B, C, and D are the only possible outcomes of an experiment, find the probability of D using the table below.

A)
B)
C)
D)

Question 15

Which number could be the probability of an event that occurs about as often as it does not occur?

A)1
B).51
C)0
D)-.51

Question 16

Fill in the blank. A(n)__________ is a collection of sample points.

A)sample space
B)event
C)experiment
D)Venn diagram

Question 17

Which number could be the probability of an event that rarely occurs?

A).01
B)-.01
C).99
D).51

Question 18

The probability of a sample point is usually taken to be the relative frequency of the occurrence of
the sample point in a very long series of repetitions of the experiment.

Question 19

In some experiments, we assign subjective probabilities, which can be interpreted as our degree of
belief in the outcome.

Question 20

An experiment consists of rolling two dice and summing the resulting values. Which of the following is not a sample point for this experiment?

A)7
B)2
C)6
D)1

Question 21

An economy pack of highlighters contains 12 yellow, 6 blue, 4 green, and 3 orange
highlighters. An experiment consists of randomly selecting one of the highlighters. Find
the probability that a blue highlighter is chosen.

Question 22

Probabilities of different types of vehicle-to-vehicle accidents are shown below: Find the probability that an accident involves a car.

A)0.30
B)0.12
C)0.58
D)0.70

Question 23

In a sample of 750 of its online customers, a department store found that 420 were men.
Use this information to estimate the probability that a randomly selected online customer
is a man.

Question 24

At a small private college with 800 students, 240 students receive some form of
government-sponsored financial aid. Find the probability that a randomly selected
student receives some form of government-sponsored financial aid.

Question 25

A hospital reports that two patients have been admitted who have contracted Crohnʹs disease. Suppose our experiment consists of observing whether each patient survives or dies as a result of
The disease. The simple events and probabilities of their occurrences are shown in the table (where
S in the first position means that patient 1 survives, D in the first position means that patient 1
Dies, etc.). Find the probability that both patients survive.

A)0.36
B)0.3025
C)0.09
D)0.55

Question 26

The accompanying Venn diagram describes the sample space of a particular experiment
and events A and B. Suppose the sample points are equally likely. Find P(A)and P(B).

Question 27

A college has 85 male and 75 female fulltime faculty members. Suppose one fulltime
faculty member is selected at random and the faculty memberʹs gender is observed.
a. List the sample points for this experiment.
b. Assign probabilities to the sample points.

Question 28

An event may contain sample points that are not in the original sample space of the experiment.
For example, the experiment of rolling two dice has the following sample space: However, the event of rolling a sum of at least 11 on the two dice is {11, 12}.

Question 29

At a community college with 500 students, 120 students are age 30 or older. Find the probability that a randomly selected student is age 30 or older.

A).76
B).24
C).30
D).12

Question 30

The probability of an event can be calculated by finding the sum of the probabilities of the
individual sample points in the event and dividing by the number of sample points in the event.

Question 31

Question 32

A clothing vendor estimates that 78 out of every 100 of its online customers do not live within 50 miles of one of its physical stores. Using this estimate, what is the probability that a randomly
Selected online customer does not live within 50 miles of a physical store?

A).22
B).78
C).28
D).50

Question 33

A bag of candy was opened and the number of pieces was counted. The results are shown in the table below: Find the probability that a randomly selected piece is either yellow or orange in color.

A)10
B)0.10
C)20
D)0.20

Question 34

Suppose that an experiment has eight equally likely outcomes. What probability is
assigned to each of the sample points?

Question 35

The manager of a warehouse club estimates that 7 out of 10 customers will donate a dollar
to help a childrenʹs hospital during an annual drive to benefit the hospital. Using the
managerʹs estimate, what is the probability that a randomly selected customer will donate
a dollar?

Question 36

A music store has 8 male and 12 female employees. Suppose one employee is selected at random and the employeeʹs gender is observed. List the sample points for this experiment, and assign
Probabilities to the sample points.

A){8, 12}; P(8)= .8 and P(12)= .12
B){male, female}; P(male)= .4 and P(female)= .6
C){8, 12}; P(8)= .5 and P(12)= .6
D){male, female}; P(male)= .8 and P(female)= .12

Question 37

A hospital reports that two patients have been admitted who have contracted Crohnʹs
disease. Suppose our experiment consists of observing whether each patient survives or
dies as a result of the disease. The simple events and probabilities of their occurrences are
shown in the table (where S in the first position means that patient 1 survives, D in the first
position means that patient 1 dies, etc.). Find the probability that neither patient survives.

Question 38

A package of self-sticking notepads contains 6 yellow, 6 blue, 6 green, and 6 pink
notepads. An experiment consists of randomly selecting one of the notepads and
recording its color. Find the sample space for the experiment.

Question 39

An experiment consists of randomly choosing a number between 1 and 10. Let A be the
event that the number chosen is less than or equal to 7. List the sample points in A.

Question 40

A hospital reports that two patients have been admitted who have contracted Crohnʹs disease. Suppose our experiment consists of observing whether each patient survives or dies as a result of
The disease. The simple events and probabilities of their occurrences are shown in the table (where
S in the first position means that patient 1 survives, D in the first position means that patient 1
Dies, etc.). Find the probability that at least one of the patients does not survive.

A)0.45
B)0.11
C)0.24
D)0.21

Question 41

n = 2, N = 5

A)10
B)6
C)20
D)3

Question 42

Three companies (A, B, and
C)are to be ranked first, second, and third in a list of
companies with the highest customer satisfaction.
a. List all the possible sets of rankings for these top three companies.
b. Assuming that all sets of rankings are equally likely, what is the probability that
Company A will be ranked first, Company B second, and Company C third?
c. Assuming that all sets of rankings are equally likely, what is the probability that
Company B will be ranked first?

Question 43

The table displays the probabilities for each of the outcomes when three fair coins are tossed and the number of heads is counted. Find the probability that the number of heads on a single toss of
The three coins is at most 2.

A).875
B).750
C).125
D).500

Question 44

An experiment consists of randomly choosing a number between 1 and 10. Let E be the event that the number chosen is even. Assuming that each of the numbers between 1 and 10 is equally likely
To be chosen, find P(E).

A).8
B).1
C).2
D).5

Question 45

The table displays the probabilities for each of the six outcomes when rolling a particular unfair die. Find the probability that the number rolled on a single roll of this die is less than 4.

A).5
B).3
C).2
D).7

Question 46

The table shows the number of each type of book found at an online auction site during a
recent search. Suppose that Juanita randomly chose one book to bid on and then noted its
type. a. List the sample points for this experiment.
b. Find the probability of each sample point.
c. What is the probability that the book was nonfiction or educational?

Question 47

A)8
B)5040
C)1
D)7

Question 48

Three fair coins are tossed and either heads (H)or tails (T)is observed for each coin.
a. List the sample points for this experiment.
b. Assign probabilities to the sample points.
c. Find the probability of the event A = {Three heads are observed}.
d. Find the probability of the event B = {Exactly two heads are observed}.
e. Find the probability of the event C = {At least two heads are observed}.

Question 49

The following data represent the scores of 50 students on a statistics exam. Suppose that
one of the 50 students is chosen at random and that studentʹs score is noted. a. What is the probability that the student's score is 88?
b. What is the probability that the student's score is less than 60?
c. What is the probability that the student's score is between 70 and 79, inclusive?

Question 50

A)3
B)6
C)2
D)1

Question 51

Two chips are drawn at random and without replacement from a bag containing three
blue chips and one red chip.
a. List the sample points for this experiment.
b. Assign probabilities to the sample points.
c. Find the probability of the event A = {Two blue chips are drawn}.
d. Find the probability of the event B = {A blue chip and a red chip are drawn}.
e. Find the probability of the event C = {Two red chips are drawn}.

Question 52

The data below show the types of medals won by athletes representing the United States
in the Winter Olympics. Suppose that one medal is chosen at random and the type of
medal noted. a. List the sample points for this experiment.
b. Find the probability of each sample point.
c. What is the probability that the medal was not bronze?

Question 53

A)5040
B)210
C)6
D)34

Question 54

A)4
B)56
C)720
D)28

Question 55

In an exit poll, 45% of voters said that the main issue affecting their choices of candidates
was the economy, 35% said national security, and the remaining 20% were not sure.
Suppose we select one of the voters who participated in the exit poll at random and ask
for the main issue affecting his or her choices of candidates.
a. List the sample points for this experiment.
b. Assign reasonable probabilities to the sample points.
c. Find the probability that the main issue affecting his or her choices was either the
economy or national security.

Question 56

n = 2, N = 10

A)45
B)19
C)8
D)90

Question 57

At a certain university, one out of every 20 students is enrolled in a statistics course. If one student at the university is chosen at random, what is the probability that the student is enrolled in a
Statistics course?

A)
B)
C)
D)

Question 58

Two chips are drawn at random and without replacement from a bag containing four blue chips and three red chips. Find the probability of drawing two red chips.

A)
B)
C)
D)

Question 59

The data show the total number of medals (gold, silver, and bronze)won by each country
winning at least one gold medal in the Winter Olympics. Suppose that one of the countries
represented is chosen at random and the total numbers of medals won by that country is
noted. a. List the sample points for this experiment.
b. Find the probability of each sample point.
c. What is the probability that the country won at least 20 total medals?

Question 60

The table shows the number of each car sold in the United States in June. Suppose the
sales record for one of these cars is randomly selected and the type of car is identified. a. List the sample points for this experiment.
b. Find the probability of each sample point.
c. What is the probability that the car was a Van or an SUV?

Question 61

Evaluate

A) 4
B) 28
C) 56
D) 16

Question 62

Evaluate

A) 1
B) 7
C) 49
D) 14

Question 63

There are 10 movies that Greg would like to rent but the store only allows him to have 4 movies at one time. In how many ways can Greg choose 4 of the 10 movies?

A)40
B)210
C)10,000
D)5040

Question 64

Compute the number of ways you can select n elements from N elements for n = 6 and N =
15.

Question 65

A pair of fair dice is tossed. Events A and B are defined as follows. A: {The sum of the numbers on the dice is 3}
B: {At least one of the dice shows a 2}
Identify the sample points in the event A ∩ B.

A){(1, 2), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (4, 2), (5, 2), (6, 2)}
B){(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)}
C){(2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (4, 2), (5, 2), (6, 2)}
D){(1, 2), (2, 1)}

Question 66

A number between 1 and 10, inclusive, is randomly chosen. Events A and B are defined as follows. A: {The number is even}
B: {The number is less than 7}
Identify the sample points in the event A ∩ B.

A){1, 2, 3, 4, 5, 6, 8, 10}
B){2, 4, 6}
C){1, 2, 3, 4, 5, 6, 7, 8, 10}
D){1, 2, 3, 4, 5, 6, 7, 9}

Question 67

The quantity 0! is defined to be equal to 0.

Question 68

A pair of fair dice is tossed. Events A and B are defined as follows. A: {The sum of the numbers on the dice is 4}
B: {The sum of the numbers on the dice is 11}
Identify the sample points in the event

A)
B)
C)
D) There are no sample points in the event

Question 69

Compute

Question 70

Evaluate

A) 1
B) 0
C) undefined
D) 6

Question 71

The manager of an advertising department has asked her creative team to propose six new
ideas for an advertising campaign for a major client. She will choose three of the six
proposals to present to the client. (We will refer to the six proposals as A, B, C, D, E, and F.)
a. In how many ways can the manager select the three of the six proposals? List the
possibilities.
b. It is unlikely that the manager will randomly select three of the six proposals, but if she
does what is the probability that she selects proposals A, D, and E?

Question 72

The combinations rule applies to situations in which the experiment calls for selecting n elements
from a total of N elements, without replacing each element before the next is selected.

Question 73

Kim submitted a list of 12 movies to an online movie rental company. The company will choose 3 of the movies and ship them to her. If all movies are equally likely to be chosen, what is the
Probability that Kim will receive the three movies that she most wants to watch? Express the
Probability as a fraction.

A)
B)
C)
D)

Question 74

Which quantity is represented on the screen below?

A)The number of sample points when a coin is flipped six times
B)The number of ways two dice can be rolled
C)The number of ways two coins can be chosen from six coins
D)The number of sample points when a die is rolled and a coin is flipped

Question 75

A number between 1 and 10, inclusive, is randomly chosen. Events A and B are defined as follows. A: {The number is even}
B: {The number is less than 7}
Identify the sample points in the event A ∪ B.

A){1, 2, 3, 4, 5, 6, 8, 10}
B){1, 2, 3, 4, 5, 6, 7, 9}
C){2, 4, 6}
D){1, 2, 3, 4, 5, 6, 7, 8, 10}

Question 76

Compute the number of ways you can select 3 elements from 7 elements.

A)343
B)10
C)35
D)21

Question 77

A pair of fair dice is tossed. Events A and B are defined as follows. A: {The sum of the numbers on the dice is 3}
B: {At least one of the dice shows a 2}
Identify the sample points in the event A ∪ B.

A){(1, 2), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)}
B){(2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (4, 2), (5, 2), (6, 2)}
C){(1, 2), (2, 1)}
D){(1, 2), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (4, 2), (5, 2), (6, 2)}

Question 78

In how many ways can a manager choose 3 of his 8 employees to work overtime helping
with inventory?

Question 79

Question 80

Which expression is equal to

A)
B)
C)
D)