Deck 3: Probability

Question 1

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

Answer 1

False

Question 2

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

A)independent
B)mutually exclusive
C)intersections
D)unions
E)dependent

Answer 2

B

Question 3

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) $\times$ P(B)
B)P(A) $\times$ P(A | B)
C)P(A)- P(A | B)
D)P(A)+ P(B)
E)P(A)+ P(B)- P(A $\cap$ B)

Answer 3

P(A) $\times$ P(B)

Question 4

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

A)divide
B)add
C)multiply
D)subtract

Question 5

An event is a collection of sample space outcomes.

Question 6

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

Question 7

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

Question 8

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 9

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

A)A random experiment
B)The sample space
C)Probability
D)A complement
E)A population

Question 10

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

Question 11

The _______ of two events A and B is another event that consists of the sample space outcomes belonging to either event A or event B,or both events A and

A)complement
B)
B)union
C)intersection
D)conditional probability

Question 12

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

Question 13

If 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 $\cap$ B)= 0
D)P(A $\cap$ B)= P(A) $\times$ P(B $\cup$ A)
E)P(A)+ P(B)= 0

Question 14

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

A)sample space
B)event
C)experiment
D)probability
E)strata

Question 15

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

Question 16

Mutually exclusive events have a nonempty intersection.

Question 17

Two mutually exclusive events having positive probabilities are ___________ dependent.

A)always
B)sometimes
C)never

Question 18

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 19

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

Question 20

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

Question 21

P( A $\cup$
B )= P( A)+ P( B)- P( A $\cap$
B )represents the formula for the

A)conditional probability.
B)addition rule.
C)addition rule for two mutually exclusive events.
D)multiplication rule.
E)subtraction theorem.

Question 22

Past company records demonstrate that 85% of new hires successfully complete their probation period.Suppose 3 newly hired individuals are randomly selected.If new hires successfully complete their probation period independently of each other,what is the probability that all will complete the probation period?

A)487
B)553
C)614
D)732
E)850

Question 23

In a study of chain saw injuries,57% involved arms or hands.If three different chain saw injury cases are randomly selected,what is the probability that they all involved arms or hands?

A)0.002
B)0.185
C)0.263
D)0.334
E)0.481

Question 24

A pharmaceutical company manufacturing pregnancy test kits wants to determine the probability of a woman not being pregnant when the test results indicate pregnancy.It is estimated that the probability of pregnancy among potential users of the kit is 10%.According to the company laboratory test results,1 out of 100 non-pregnant women tested pregnant (false positive).On the other hand,1 out of 200 pregnant women tested non-pregnant (false negative).A woman has just used the pregnancy test kit manufactured by the company and the results showed pregnancy.What is the probability that she is not pregnant?

A)0.9
B)0.009
C)0.083
D)0.917
E)0.1085

Question 25

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)0.122
B)0.393
C)0.544
D)0.287
E)0.621

Question 26

In a large organization,55% of all employees are female,25% of the employees have a business degree,and 40% of all males have a business degree.What is the percentage of employees who are female with a business degree?

A)2%
B)5%
C)7%
D)9%
E)11%

Question 27

If events A and B are mutually exclusive,then P(A | B)= _____.

A)00
B)13
C)22
D)50
E)99

Question 28

In a large organization,55% of all employees are female,25% of the employees have a business degree,and 40% of all males have a business degree.What is the probability that one randomly selected employee will be either a female or have a business degree?

A)0.29
B)0.41
C)0.67
D)0.73
E)0.83

Question 29

Container 1 has 8 items,3 of which are defective.Container 2 has 5 items,2 of which are defective.One item is selected at random from each container.What is the probability that exactly one of the two items is defective?

A)0.25
B)0.275
C)0.325
D)0.475
E)0.575

Question 30

Peter is considering pursuing an MBA degree.He has applied to two different universities.The acceptance rate for applicants with similar qualifications is 25% for University A and 40% for University B.What is the probability that Peter will not be accepted at either university? You may assume that the universities make their decisions independently of one another.

A)15
B)25
C)35
D)45

Question 31

A pharmaceutical company manufacturing pregnancy test kits wants to determine the probability of a woman actually being pregnant when the test results indicate that she is not pregnant.It is estimated that the probability of pregnancy among potential users of the kit is 10%.According to the company laboratory test results,1 out of 100 non-pregnant women tested pregnant (false positive).On the other hand,1 out of 200 pregnant women tested non-pregnant (false negative).A woman has just used the pregnancy test kit manufactured by the company and the results showed that she is not pregnant.What is the probability that she is pregnant?

A)0.01
B)0.009
C)0.0005
D)0.083
E)0.00056

Question 32

What is the probability that an insured driver of any age will be involved in an accident?

A)0.35
B)0.205
C)0.65
D)0.983
E)0.795

Question 33

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

A)0.286
B)0.067
C)0.007
D)0.368
E)0.143

Question 34

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.Assuming that the parts function independently of each other,what is the probability that a machine is non-defective?

A)0.8330
B)0.7265
C)0.9029
D)0.9815
E)0.8902

Question 35

An accident has just been reported.What is the probability that the insured driver is under the age of 25?

A)0.35
B)0.205
C)0.14
D)0.683
E)0.4

Question 36

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

A)1/4
B)1/6
C)1/8
D)1/12
E)1/16

Question 37

In a large organization,55% of all employees are female,25% of the employees have a business degree,and 40% of all males have a business degree.What is the probability that an employee has a business degree given that the employee is a female?

A)0.127
B)0.355
C)0.250
D)0.465
E)0.282

Question 38

If A and B are independent events,and P( A)= .2,and P(B )= .7,then P(A $\cup$
B )_{= _____.}

A)91
B)47
C)86
D)14
E)76

Question 39

The management believes that the weather conditions significantly affect the level of demand.48 monthly sales reports are randomly selected.These monthly sales reports showed 15 months with high demand,28 months with medium demand,and 5 months with low demand.12 of the 15 months with high demand had favorable weather conditions.14 of the 28 months with medium demand had favorable weather conditions.Only 1 of the 5 months with low demand had favorable weather conditions.What is the probability that weather conditions are poor,given that the demand is high?

A)2
B)5
C)8
D)25
E)75

Question 40

The management believes that the weather conditions significantly impact the level of demand and the estimated probabilities of poor weather conditions given different levels of demand is presented below. $$\text { P (Poor } \mid \text { High } ) = .2 , \text { P(Poor } \mid \text { Medium } ) = .5 , \text { P } ( \text { Poor } \mid \text { Low } ) = .8$$

P(High)= 15/48,P(Medium)= 28/48,P(Low)= 5/48
What is the probability of high demand given that the weather conditions are poor?

A)06
B)44
C)1429
D)12
E)1818

Question 41

Consider the experiment of tossing four coins and observing the face of the coin,heads or tails,that appears each time.How many outcomes are in the sample space?

A)2
B)4
C)6
D)12
E)16

Question 42

Container 1 has 8 items,3 of which are defective.Container 2 has 5 items,2 of which are defective.One item is selected at random 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)225
B)006
C)399
D)521
E)178

Question 43

Container 1 has 8 items,3 of which are defective.Container 2 has 5 items,2 of which are defective.One item is selected at random from each container.What is the probability that both items are not defective?

A)003
B)098
C)246
D)375
E)539

Question 44

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

Question 45

A lot contains 12 items,4 of which are defective.If three items are drawn at random from the lot,what is the probability that none of them are defective?

A)6667
B)6363
C)6000
D)3003
E)2545

Question 46

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

Question 47

A probability may be interpreted as a long-run _____ frequency.

Question 48

The _____ is the set of all of the distinct possible outcomes of an experiment.

Question 49

If you roll a pair of fair dice,what is the probability that the number of dots on the two dice will sum to nine or higher?

A)0003
B)0095
C)1334
D)2778
E)3446

Question 50

Susan is considering pursuing an MBA degree.She has applied to two different universities.The acceptance rate for applicants with similar qualifications is 25% for University A and 40% for University B.What is the probability that Susan will be accepted at University A and rejected at University B? You may assume that the universities make their decisions independently of one another.

A)15
B)03
C)19
D)22

Question 51

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

Question 52

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

A)0004951
B)0002505
C)0149980
D)0253533
E)0444967

Question 53

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

A)7/8
B)1/2
C)3/8
D)6/8
E)1/8

Question 54

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

Question 55

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

Question 56

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)27
B)39
C)41
D)52
E)69

Question 57

If you draw a card from a standard deck of 52 cards,what is the probability that you obtain a King?

A)1/52
B)1/26
C)1/21
D)1/13
E)1/4

Question 58

Suppose that you believe that the probability you will get a grade of B or better in Introduction to Finance is 0.6,and the probability that you will get a grade of B or better in Introduction to Accounting is 0.5.If these events are independent,what is the probability that you will be a grade of B or better in both courses?

A)03
B)25
C)30
D)43
E)50

Question 59

If you roll a pair of fair dice,what is the probability that the number of dots on the two dice will sum to seven?

A)1/16
B)1/8
C)1/6
D)1/4
E)1/2

Question 60

If you roll a fair die,what is the probability that an even number of dots appear?

A)05
B)20
C)25
D)50
E)75

Question 61

A lot contains 10 items,3 of which are defective.If three items are drawn at random from the lot,what is the probability that none of them are defective?

Question 62

Consider the experiment of rolling three dice and observing the number of dots that appear each time.How many outcomes are in the sample space?

Question 63

If you roll a fair die,what is the probability that at least 5 dots appear?

Question 64

The _______ of two events A and B is the event that consists of the sample space outcomes belonging to both event A and event B.

Question 65

In the application of Bayes' theorem the sample information is combined with prior probabilities to obtain ___________________ probabilities.

Question 66

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

Question 67

If you draw a card from a standard deck of 52 cards,what is the probability that you obtain a face card (i.e.a Jack,Queen,or King)?

Question 68

Consider the experiment of rolling three dice and observing the number of dots that appear each time.What is the probability that at least one of the three dice shows an even number of dots?

Question 69

What is the probability that both items are not defective?

Question 70

__________________ statistics is an area of statistics that uses Bayes' theorem to update prior belief about a probability or population parameter to a posterior belief.

Question 71

A group has 10 men and 6 women.If 3 people are selected at random from the group,what is the probability that they are all men?

Question 72

If you roll a pair of fair dice,what is the probability that the number of dots on the two dice will sum to five?

Question 73

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

Question 74

A person is dealt 4 cards from a deck of 52 cards.What is the probability they are all clubs?

Question 75

What is the probability that the item from container one is defective and the item from container 2 is not defective?

Question 76

If you roll a pair of fair dice,what is the probability that the number of dots on the two dice will sum to eight or higher?

Question 77

The _______ of two events A and B is another event that consists of the sample space outcomes belonging to either event A or event B,or both events A and B.

Question 78

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

Question 79

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

Question 80

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