Deck 4: Probability

Question 1

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

Answer 1

False

Question 2

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

Answer 2

True

Question 3

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

Answer 3

False

Question 4

Mutually exclusive events have a nonempty intersection.

Question 5

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 6

An event is a collection of sample space outcomes.

Question 7

A ____________ 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 8

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

Question 9

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

Question 10

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)P(A
D)P(A

Question 11

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

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

Question 12

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) $\bullet$ P(B)
B)P(A) $\bullet$ P(A|B)
C)P(B) $\bullet$ P(A|B))
D)All of the above are correct

Question 13

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 event X and Y.

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

Question 14

___________________ 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 15

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

Question 16

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)½
C)1/6
D)0
E)1/3

Question 17

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

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

Question 18

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

Question 19

Two mutually exclusive events having positive probabilities are ______________ dependent.

A)Always
B)Sometimes
C)Never

Question 20

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

Question 21

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 22

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 23

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 24

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 25

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 26

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

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

Question 27

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

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

Question 28

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 29

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

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

Question 30

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 31

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 32

P(A B)= P(A)+ P(B)- P(A B)represents the formula for the

A)conditional probability
B)addition rule
C)addition rule for two mutually exclusive events
D)multiplication rule

Question 33

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 34

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

A)P(B)
B)P(A $\cap$ B)
C)P(A)
D)P(A U B)

Question 35

The simultaneous occurrence of event A and B is represented by the notation: _______.

A)A U B
B)A│B
C)A
D)B│A

Question 36

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 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

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

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

Question 40

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 41

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

A)0.999
B)0.001
C)0.002
D)0.998
E)0.500

Question 42

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 43

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 44

Suppose P(A)= .45,P(B)= .20,P(C)= .35,P(E|A)= .10,P(E|B)= .05,and P(E|C)= 0.What is P(E)?

A)0.222
B)0.150
C)0.855
D)0.315
E)0.055

Question 45

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 46

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 one 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 47

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 48

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 49

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 one of the items is defective?

A)0.2250
B)0.3000
C)0.0250
D)0.4500
E)0.1500

Question 50

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 51

Suppose P(A)= .45,P(B)= .20,P(C)= .35,P(E|A)= .10,P(E|B)= .05,and P(E|C)= 0.What is P(A|E)?

A)0.045
B)0.190
C)0.818
D)0.100
E)0.055

Question 52

A person has 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 53

A machine is made up of 3 components: an upper part,a mid part,and a lower part.The machine is then assembled.5 percent of the upper parts are defective;4 percent of the mid parts are defective;1 percent of the lower parts are defective.What is the probability that a machine is non-defective?

A)0.100
B)0.903
C)0.900
D)0.0002
E)0.912

Question 54

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 55

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 56

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 57

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 58

Suppose P(A)= .45,P(B)= .20,P(C)= .35,P(E|A)= .10,P(E|B)= .05,and P(E|C)= 0.What is P (C|E)?

A)1
B)0.055
C)0.032
D)0
E)0.005

Question 59

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 60

Suppose P(A)= .45,P(B)= .20,P(C)= .35,P(E|A)= .10,P(E|B)= .05,and P(E|C)= 0.What is P(B|E)?

A)0.182
B)0.010
C)0.050
D)0.065
E)0.055

Question 61

If events A and B are mutually exclusive,calculate P(A|B).

A)Can't be determined
B)0
C)1
D)0.50

Question 62

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 63

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

Question 64

An urn contains five white,three red,and four black balls.Three are drawn at random without replacement. 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 65

What is the probability of rolling a six with a fair die five times in a row?

A)1/6
B)1/46,656
C)1/7,776
D)5/7,776

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 buys beer.

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

Question 67

Employees of a local university have been classified according to gender and job type. If an employee is selected at random what is the probability that the employee is female or works as an hourly staff member?

A)0.133
B)0.533
C)0.667
D)0.400
E)0.333

Question 68

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 69

If P(A B)= .3 and P(A|B)= .9,find P(B).

A)0.6
B)0.3
C)0.5
D)0.27
E)0.33

Question 70

Which of the following are properties of a valid discrete probability distribution?

A)p(X)
B) $\Sigma$ p(X)= 1
C)A only
D)B only
E)A and B

Question 71

Employees of a local university have been classified according to gender and job type. If an employee is selected at random what is the probability that the employee is female given that the employee is a salaried member of staff?

A).167
B).500
C).625
D)267
E).375

Question 72

Employees of a local university have been classified according to gender and job type. If an employee is selected at random what is the probability that the employee is a member of the hourly staff given that the employee is female?

A)0.400
B)0.133
C)0.160
D)0.053
E)0.533

Question 73

Employees of a local university have been classified according to gender and job type. If an employee is selected at random what is the probability that the employee is male?

A).667
B).367
C).333
D).500
E).917

Question 74

If A and B are independent events,P(A)= .2,and P(B)= .7,determine P(A B)

A)0.90
B)0.14
C)0.76
D)0.50
E)0.24

Question 75

Employees of a local university have been classified according to gender and job type. If an employee is selected at random what is the probability that the employee is female or works as a member of the faculty?

A)0.73
B)0.08
C)0.33
D)0.70
E)0.05

Question 76

How many times must a die be tossed if the expected number of ones is five?

A)5
B)30
C)35
D)6

Question 77

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 78

Employees of a local university have been classified according to gender and job type. If an employee is selected at random what is the probability that the employee is male and salaried staff?

A).15
B).10
C).38
D).50
E).85

Question 79

If a product is made using five individual components,and P(product meets specifications)= P(E)= .98,what is the probability of an individual component meeting specifications assuming that this probability is the same for all five components?

A)0.98
B)0.996
C)0.004
D)0.02
E)0.904

Question 80

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