Deck 4: Probability

Question 1

Bayes' Theorem uses prior probabilities with additional information to compute posterior probabilities.

Answer 1

True

Question 2

Mutually exclusive events have a nonempty intersection.

Answer 2

False

Question 3

The probability of an event is the sum of the probabilities of the sample space outcomes that correspond to the event.

Answer 3

True

Question 4

If events A and B are mutually exclusive,then P(A|B)is always equal to zero.

Question 5

If two events are independent,we can _____________ their probabilities to determine the intersection probability.

A)Divide
B)Add
C)Multiply
D)Subtract

Question 6

Two mutually exclusive events having positive probabilities are ______________ dependent.

A)Always
B)Sometimes
C)Never

Question 7

Bayes' Theorem is always based on two states of nature and three experimental outcomes.

Question 8

___________________ is a measure of the chance that an uncertain event will occur.

A)Random experiment
B)Sample space
C)Probability
D)A complement
E)A population

Question 9

If events A and B are mutually exclusive,then $\mathrm { P } ( \mathrm { A } \cap \mathrm { B } )$
is always equal to zero.

Question 10

A subjective probability is a probability assessment that is based on experience,intuitive judgment,or expertise.

Question 11

Events that have no sample space outcomes in common,and therefore cannot occur simultaneously,are referred to as independent events.

Question 12

The method of assigning probabilities when all outcomes are equally likely to occur is called the classical method.

Question 13

Two events are independent if the probability of one event is influenced by whether or not the other event occurs.

Question 14

The set of all possible experimental outcomes is called a(n)____________.

A)Sample space
B)Event
C)Experiment
D)Probability

Question 15

A contingency table is a tabular summary of probabilities concerning two sets of complementary events.

Question 16

Events that have no sample space outcomes in common,and therefore cannot occur simultaneously,are ____________.

A)Independent
B)Mutually exclusive
C)Intersections
D)Unions

Question 17

An event is a collection of sample space outcomes.

Question 18

If events A and B are independent,then P(A|B)is always equal to zero.

Question 19

A manager has just received the expense checks for six of her employees.She randomly distributes the checks to the six employees.What is the probability that exactly five of them will receive the correct checks (checks with the correct names)?

A)1
B)1/2
C)1/6
D)0
E)1/3

Question 20

If events A and B are independent,then the probability of simultaneous occurrence of event A and event B can be found with ____________.

A)P(A)●P(B)
B)P(A)●P(B|A)
C)P(B)●P(A|B)
D)All of these are correct.

Question 21

The simultaneous occurrence of events A and B is represented by the notation _______________.

A) $A \cup B$
B)A?B
C) $A \cap B$
D)B?A

Question 22

Determine whether the two events are mutually exclusive.
Unmarried person and a person with an employed spouse

A)Mutually exclusive
B)Not mutually exclusive

Question 23

Probabilities must be assigned to experimental outcomes so that the probabilities of all the experimental outcomes add up to _____________.

A)1
B)Between 0 and 1
C)Between -1 and 1
D)0

Question 24

If P(A)> 0 and P(B)> 0 and events A and B are independent,then ____________.

A)P(A)= P(B)
B)P(A|B)= P(A)
C) $\mathrm { P } ( \mathrm { A } \cap \mathrm { B } ) = 0$
D) $\mathrm { P } ( \mathrm { A } \cap \mathrm { B } ) = \mathrm { P } ( \mathrm { A } ) \mathrm { P } ( \mathrm { B } \cup \mathrm { A } )$

Question 25

Determine whether the two events are mutually exclusive.
Someone born in the United States and a US citizen

A)Mutually exclusive
B)Not mutually exclusive

Question 26

When the probability of one event is not influenced by whether or not another event occurs,the events are said to be _____________.

A)Independent
B)Dependent
C)Mutually exclusive
D)Experimental

Question 27

Probabilities must be assigned to experimental outcomes so that the probability assigned to each experimental outcome must be between ____________,inclusive.

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

Question 28

The __________ of event X consists of all sample space outcomes that do not correspond to the occurrence of event X.

A)Independence
B)Complement
C)Conditional probability
D)Dependence

Question 29

A(n)_______________ probability is a probability assessment that is based on experience,intuitive judgment,or expertise.

A)Experimental
B)Relative frequency
C)Objective
D)Subjective

Question 30

Determine whether the two events are mutually exclusive.
Consumer with an unlisted phone number and a consumer who does not drive

A)Mutually exclusive
B)Not mutually exclusive

Question 31

The _____________ of an event is a number that measures the likelihood that an event will occur when an experiment is carried out.

A)Outcome
B)Probability
C)Intersection
D)Observation

Question 32

A(n)____________ is the probability that one event will occur given that we know that another event already has occurred.

A)Sample space outcome
B)Subjective probability
C)Complement of events
D)Long-run relative frequency
E)Conditional probability

Question 33

If events A and B are independent,then P(A|B)is equal to _____________.

A)P(B)
B)P(A ? B)
C)P(A)
D) $P ( A \cup B )$

Question 34

When the probability of one event is influenced by whether or not another event occurs,the events are said to be _____________.

A)Independent
B)Dependent
C)Mutually exclusive
D)Experimental

Question 35

A(n)_____________ is the set of all of the distinct possible outcomes of an experiment.

A)Sample space
B)Union
C)Intersection
D)Observation

Question 36

Determine whether the two events are mutually exclusive.
Voter who favors gun control and an unregistered voter

A)Mutually exclusive
B)Not mutually exclusive

Question 37

A probability may be interpreted as a long run _____________ frequency.

A)Observational
B)Relative
C)Experimental
D)Conditional

Question 38

A process of observation that has an uncertain outcome is referred to as a(n)_____________.

A)Probability
B)Frequency
C)Conditional probability
D)Experiment

Question 39

The ___________ of two events X and Y is another event that consists of the sample space outcomes belonging to either event X or event Y or both events X and Y.

A)Complement
B)Union
C)Intersection
D)Conditional probability

Question 40

A(n)______________ is a collection of sample space outcomes.

A)Experiment
B)Event
C)Set
D)Probability

Question 41

A coin is tossed 6 times.What is the probability that at least one head occurs?

A)63/64
B)1/64
C)1/36
D)5/6
E)1/2

Question 42

What is the probability of rolling a value higher than eight with a pair of fair dice?

A)6/36
B)18/36
C)10/36
D)8/36
E)12/36

Question 43

Consider a standard deck of 52 playing cards,a randomly selected card from the deck,and the following events: R = red,B = black,A = ace,N = nine,D = diamond,and C = club.
Are R and A mutually exclusive?

A)Yes,mutually exclusive
B)No,not mutually exclusive

Question 44

If we consider the toss of four coins as an experiment,how many outcomes does the sample space consist of?

A)8
B)4
C)16
D)32
E)2

Question 45

Consider a standard deck of 52 playing cards,a randomly selected card from the deck,and the following events: R = red,B = black,A = ace,N = nine,D = diamond,and C = club.
Are A and N mutually exclusive?

A)Yes,mutually exclusive
B)No,not mutually exclusive

Question 46

Consider a standard deck of 52 playing cards,a randomly selected card from the deck,and the following events: R = red,B = black,A = ace,N = nine,D = diamond,and C = club.
Are D and C mutually exclusive?

A)Yes,mutually exclusive
B)No,not mutually exclusive

Question 47

A lot contains 12 items,and 4 are defective.If three items are drawn at random from the lot,what is the probability they are not defective?

A)0.3333
B)0.2545
C)0.5000
D)0.2963
E)0.0370

Question 48

What is the probability of at least one tail in the toss of three fair coins?

A)1/8
B)4/8
C)5/8
D)7/8
E)6/8

Question 49

What is the probability that an even number appears on the toss of a die?

A)0.5
B)0.33
C)0.25
D)0.67
E)1.00

Question 50

Determine whether the two events are mutually exclusive.
Someone with three sisters and someone with four siblings

A)Mutually exclusive
B)Not mutually exclusive

Question 51

Consider a standard deck of 52 playing cards,a randomly selected card from the deck,and the following events: R = red,B = black,A = ace,N = nine,D = diamond,and C = club.
Are R and C mutually exclusive?

A)Yes,mutually exclusive
B)No,not mutually exclusive

Question 52

Container 1 has 8 items,3 of which are defective.Container 2 has 5 items,2 of which are defective.If one item is drawn from each container:
What is the probability that only one of the items is defective?

A)0.2250
B)0.3000
C)0.0250
D)0.4000
E)0.1500

Question 53

A person is dealt 5 cards from a deck of 52 cards.What is the probability they are all clubs?

A)0.2500
B)0.0962
C)0.0769
D)0.0010
E)0.0005

Question 54

What is the probability that a king appears in drawing a single card from a deck of 52 cards?

A)4/13
B)1/13
C)1/52
D)1/12
E)2/13

Question 55

What is the probability of rolling a seven with a pair of fair dice?

A)6/36
B)3/36
C)1/36
D)8/36
E)7/36

Question 56

Container 1 has 8 items,3 of which are defective.Container 2 has 5 items,2 of which are defective.If one item is drawn from each container:
What is the probability that both items are not defective?

A)0.3750
B)0.3846
C)0.1500
D)0.6154
E)0.2000

Question 57

Container 1 has 8 items,3 of which are defective.Container 2 has 5 items,2 of which are defective.If one item is drawn from each container:
What is the probability that the item from Container 1 is defective and the item from Container 2 is not defective?

A)0.3846
B)0.2250
C)0.3750
D)0.6154
E)0.1500

Question 58

A group has 12 men and 4 women.If 3 people are selected at random from the group,what is the probability that they are all men?

A)0.4219
B)0.5143
C)0.3929
D)0.0156
E)0.0045

Question 59

Given the standard deck of cards,what is the probability of drawing a red card,given that it is a face card?

A)0.500
B)0.115
C)0.231
D)0.077
E)0.308

Question 60

Consider a standard deck of 52 playing cards,a randomly selected card from the deck,and the following events: R = red,B = black,A = ace,N = nine,D = diamond,and C = club.
Are N and C mutually exclusive?

A)Yes,mutually exclusive
B)No,not mutually exclusive

Question 61

At a college,70 percent of the students are women,and 50 percent of the students receive a grade of C.25 percent of the students are neither female nor C students.Use this contingency table.
$\begin{array} { l c c c } & \mathrm { C } & \overline { \mathrm { C } } & \\\text { Women } & .45 & .25 & .70 \\\text { Men } & .05 & .25 & .30 \\& .50 & 50 & 1.00\end{array}$

A)0.05
B)0.10
C)0.30
D)0.17
E)0.50

Question 62

At a college,70 percent of the students are women,and 50 percent of the students receive a grade of C.25 percent of the students are neither female nor C students.Use this contingency table.
$\begin{array} { l c c r } & \mathrm { C } & \overline { \mathrm { C } } & \\\text { Women } & .45 & .25 & .70 \\\text { Men } & .05 & .25 & .30 \\& .50 & .50 & 1.00\end{array}$

A).45
B).50
C).70
D).25
E).05

Question 63

What is the probability that any two people chosen at random were born on the same day of the week?

A)1/7
B)1/49
C)2/7
D)2/49

Question 64

At a college,70 percent of the students are women,and 50 percent of the students receive a grade ofC.25 percent of the students are neither female nor C students.Use this contingency table.
$\begin{array} { l c c r } & \mathrm { C } & \overline { \mathrm { C } } & \\\text { Women } & .45 & .25 & .70 \\\text { Men } & .05 & .25 & .30 \\& .50 & .50 & 1.00\end{array}$

A).45
B).50
C).70
D).25
E).05

Question 65

A card is drawn from a standard deck.Given that a face card is drawn,what is the probability it will be a king?

A)1/3
B)1/13
C)4/13
D)1/12
E)1/4

Question 66

Two percent (2%)of the customers of a store buy cigars.Half of the customers who buy cigars buy beer.25 percent who buy beer buy cigars.Determine the probability that a customer neither buys beer nor buys cigars.

A)0.98
B)0.95
C)0.75
D)0.96
E)0.50

Question 67

A card is drawn from a standard deck.What is the probability the card is an ace,given that it is a club?

A)1/52
B)1/13
C)4/13
D)1/4

Question 68

A family has two children.What is the probability that both are girls,given that at least one is a girl?

A)1/8
B)1/4
C)1/2
D)1/3
E)1/6

Question 69

A machine is made up of 3 components: an upper part,a middle part,and a lower part.The machine is then assembled.5 percent of the upper parts are defective,4 percent of the middle parts are defective,and 1 percent of the lower parts are defective.What is the probability that a machine is not defective?

A)0.100
B)0.929
C)0.800
D)0.0002
E)0.729

Question 70

An urn contains five white,three red,and four black balls.Three are drawn at random and not placed back into the urn.What is the probability that no ball is red?

A)0.7500
B)0.0156
C)0.2917
D)0.4219
E)0.3818

Question 71

A machine is produced by a sequence of operations.Typically,one defective machine is produced per 1000 parts.What is the probability of two nondefective machines being produced?

A)0.000999
B)0.001
C)0.002
D)0.998
E)0.500

Question 72

Independently,a coin is tossed,a card is drawn from a deck,and a die is thrown.What is the probability of observing a head on the coin,an ace on the card,and a five on the die?

A)0.0064
B)0.1000
C)0.7436
D)0.0096
E)0.5000

Question 73

At a college,70 percent of the students are women,and 50 percent of the students receive a grade of C.25 percent of the students are neither female nor C students.Use this contingency table.
$\begin{array} { l c c c } & \mathrm { C } & \overline { \mathrm { C } } & \\\text { Women } & .45 & .25 & .70 \\\text { Men } & .05 & .25 & .30 \\& .50 & 50 & 1.00\end{array}$

A)0.05
B)0.10
C)0.30
D)0.17
E)0.50

Question 74

The probability of event A occurring given that event B has already occurred is 0.61.The probability of both events occurring is 0.5.What is the probability of event B occurring?

A)0.305
B)0.195
C)0.390
D)0.820
E)0.500

Question 75

At a college,70 percent of the students are women and 50 percent of the students receive a grade of C.25 percent of the students are neither female nor C students.Use this contingency table.
$\begin{array} { l c l r } & \mathrm { C } & \overline { \mathrm { C } } & \\\text { Women } & .45 & .25 & .70 \\\text { Men } & .05 & .25 & .30 \\& .50 & .50 & 1.00\end{array}$

A)0.45
B)0.90
C)0.70
D)0.64
E)0.50

Question 76

Given a standard deck of cards,what is the probability of drawing a face card,given that it is a red card?

A)0.115
B)0.500
C)0.231
D)0.462
E)0.308

Question 77

A letter is drawn from the alphabet of 26 letters.What is the probability that the letter drawn is a vowel?

A)5/26
B)1/26
C)4/26
D)21/26

Question 78

A pair of dice is thrown.What is the probability that one of the faces is a 3,given that the sum of the two faces is 9?

A)1/3
B)1/36
C)1/6
D)1/2
E)1/4

Question 79

Two percent (2%)of the customers of a store buy cigars.Half of the customers who buy cigars buy beer.25 percent who buy beer buy cigars.Determine the probability that a customer buys beer.

A)0.25
B)0.01
C)0.04
D)0.50
E)0.005

Question 80

What is the probability of winning four games in a row,if the probability of winning each game individually is 1/2?

A)1/4
B)1/8
C)1/2
D)3/16
E)1/16