Deck 16: Probability

Question 1

What is the difference between an event and an outcome?

A)The event will definitely occur, whereas the outcome may or may not.
B)Outcomes never occur, whereas events do.
C)In a given situation, there are many possible events, and the outcome is the one for which we want to know the probability.
D)In a given situation, there are many possible outcomes, and an event is the outcome or set of outcomes for which we want to know the probability.
E)There is no difference.The two terms are used interchangeably.

Answer 1

D

Question 2

What is a favorable outcome?

A)an outcome that we expect to occur
B)an outcome that we know will definitely occur
C)an outcome included in the event
D)an outcome excluded from the event
E)an outcome that is found to be pleasing

Answer 2

C

Question 3

Which method for establishing probability would be most appropriate for determining the probability that someone will develop a technique for producing cold fusion in your lifetime?

A)method of equal alternatives
B)method of frequency
C)intuitive judgment
D)The methods would all be equally appropriate.
E)None of the methods could be applied in this situation.

Answer 3

C

Question 4

What does it mean if something has a probability of 1?

A)It is very unlikely to occur.
B)It is very likely to occur.
C)It must occur.
D)It cannot occur.
E)We have no information about whether or not it will occur.

Question 5

The notation p(A) stands for the probability that:

A)event p will occur
B)event A will occur
C)event p will occur A times
D)event A will occur p times
E)events p and A will occur at the same time

Question 6

Can every probability be expressed in more than one way?

A)Yes, although one way of expressing the probability is always more precise than the others.
B)Yes, and with equal precision.
C)No, because it is possible to convert percentages to odds, but not odds to percentages.
D)No, because it is possible to convert odds to percentages, but not percentages to odds.
E)No, because it is only possible to express each probability in exactly one way.

Question 7

In general, a probability tells us:

A)which things will not happen
B)which things will happen
C)which things will happen and which things will not happen
D)which things will happen or which things will not happen
E)how likely things are to happen

Question 8

An outcome or set of outcomes for which we want to know the probability is technically called a(n):

A)event
B)result
C)yield
D)achievement
E)possibility

Question 9

When a probability is expressed as a fraction, it must be a number between:

A)-1 and 1
B)0 and 1
C)1 and 2
D)-10 and 10
E)1/2 and 1

Question 10

One way to formulate the probability of drawing a queen from a deck of cards is to say that there is a 1 in 13 chance.Another common way to say the same thing is to say that:

A)there are four queen events
B)a queen event will only occur between 1:12 and 1:13
C)the odds are between the chances of drawing a jack or a king
D)the odds are 1:13
E)the odds are 1:12

Question 11

Which of the following statements expresses a probability?

A)Callista gets a 12% annual return on her investment.
B)The new shop is open from nine to five.
C)Buying brand name groceries can cost 8% more than buying the store brand.
D)On this diet, I lose two pounds per week.
E)There is a 43% chance that a donor will be found in time.

Question 12

Which is the most complete and accurate list of the methods used to establish probability?

A)method of equal alternatives, method of frequency
B)method of frequency, intuitive judgment, random projection
C)method of equal alternatives, method of frequency, intuitive judgment
D)intuitive judgment, random projection
E)intuitive judgment, random projection, method of equal alternatives

Question 13

Which method for establishing probability would be most appropriate for determining the probability that before the end of the 21st century there will be an American president of Asian descent?

A)method of equal alternatives
B)method of frequency
C)intuitive judgment
D)The methods would all be equally appropriate.
E)None of the methods could be applied in this situation.

Question 14

Which method for establishing probability would be most appropriate for determining the probability that the next four books randomly selected from a library will all contain an odd number of words?

A)method of equal alternatives
B)method of frequency
C)intuitive judgment
D)The methods would all be equally appropriate.
E)None of the methods could be applied in this situation.

Question 15

Suppose that you secretly choose a number between one and one hundred, and ask a friend to guess that number.One way to formulate the probability of your friend guessing your number on the first try is to say that there is a 1% chance.Another common way to say the same thing is to say that:

A)it is impossible
B)the odds are 1 in 99
C)the odds are 1:99
D)the odds are 100 to 1 against
E)the odds are 100 to 1 for

Question 16

Which of the following statements expresses a probability?

A)One entry out of every 300 will win a prize.
B)Two members of the book club are dominating the discussion.
C)A coin was flipped four times and the results were recorded.
D)A meteoroid could strike the Earth in the next 20 years.
E)The painting is likely to fetch at least $2,000 at auction.

Question 17

Which of the following statements expresses a probability?

A)Toby is 5 inches taller than Rita.
B)There are fourteen singers in the choir.
C)There's a 60% chance of rain this evening.
D)When two dice are rolled, there are 36 possible outcomes.
E)Maya may or may not stop by to pick up her book tonight.

Question 18

What does it mean if something has a probability of 1%?

A)It is very unlikely to occur.
B)It is very likely to occur.
C)It must occur.
D)It cannot occur.
E)We have no information about whether or not it will occur.

Question 19

Outcomes that are not included in an event are called:

A)outliers
B)unfavorable
C)exclusions
D)disjunctive
E)flies in the ointment

Question 20

What does it mean if something has a probability of 0?

A)It is very unlikely to occur.
B)It is very likely to occur.
C)It must occur.
D)It cannot occur.
E)We have no information about whether or not it will occur.

Question 21

Can every method of establishing probability be used in every situation?

A)Yes, because none of them requires any special conditions.
B)Yes, but one of them will usually be preferable to the others.
C)Yes, but different people will prefer different methods in each case.
D)No, because some methods require special conditions that might not be met.
E)No, because in each situation, it is only possible to apply one of the methods.

Question 22

We can only apply the method of equal alternatives when the number of alternative outcomes is:

A)known
B)unknown
C)even
D)odd
E)equal to the number of events

Question 23

Which of the following probabilities would be best determined by using the method of equal alternatives?

A)the odds that the next car that passes will be white
B)the odds that the proper diagnosis for a patient is diabetes
C)the odds that a flipped coin will land heads up 10 times in a row
D)the odds that a 35-year-old woman will die during the term of her life insurance policy
E)the odds that a nuclear reactor will fail

Question 24

Some probabilities are established simply by an individual's assessment of the situation.Such an assessment is technically called a(n):

A)subjective assessment
B)individual assessment
C)individual hunch
D)intuitive judgment
E)guesstimation

Question 25

Which of the following probabilities would be best determined by using the method of frequency?

A)the odds that a certain dog will live to be 15 years old
B)the odds that a marble dropped onto a flat table will roll off its left side
C)the odds that a randomly chosen chess piece will be a bishop
D)the odds that a new variety of cheese will taste good
E)the odds that a bee randomly selected from a beehive will be the queen

Question 26

Which of the following probabilities would be best determined by using the method of equal alternatives?

A)the odds that a certain battery will last for another hour
B)the odds that a bacterial infection will respond to the first round of antibiotics
C)the odds that a cat's next litter will have four kittens
D)the odds that the sound in your attic is a raccoon
E)the odds that, at a certain time, a certain cow will be facing east, rather than any of the other three directions

Question 27

Which of the following probabilities would be best determined by using the method of frequency?

A)the odds that a certain turtle will be a reptile
B)the odds that a certain turtle will be an albino
C)the odds that a certain turtle will take an even number of bites to eat a large piece of lettuce
D)the odds that a certain turtle will spontaneously begin to speak
E)the odds that a certain turtle will be dealt an 18 in blackjack

Question 28

Is it possible to establish the probability of an event that has already occurred?

A)No, because by its very nature, probability only applies to future events.
B)No, because after an event has occurred, we can't determine what all of the other possible outcomes might have been.
C)Yes, since we could still determine how likely the outcome was, relative to the other outcomes that might have occurred.
D)Yes, but we can only consider the probability to be 1, since the event definitely happened.
E)Yes, but the probability cannot be established as precisely as it could have been before the event occurred.

Question 29

Which of the following probabilities would be best determined by using the method of frequency?

A)the odds that someone who rolls two dice will roll a 9
B)the odds that it will rain tomorrow
C)the odds that the spinner in a game of Twister will be pointing to yellow when it stops
D)the odds of winning the lottery
E)the odds of being dealt a full house in a game of poker

Question 30

The method of frequency assigns probability by finding the frequency with which:

A)the event is represented in a list of the possible outcomes
B)previous researchers have failed to determine the correct probability
C)research done by others has measured an approximately similar probability
D)a given outcome has failed to occur in a reference group of randomly chosen cases
E)a given outcome has occurred in a reference group of similar cases

Question 31

Which of the following probabilities would be best determined by using the method of equal alternatives?

A)the odds that a certain competitor will win the gold medal at the Olympics
B)the odds that a banana will have brown spots 24 hours from now
C)the odds that the next business to open in a certain town will be a grocery store
D)the odds that a certain monkey can be housebroken
E)the odds that a letter randomly chosen from the English alphabet will be a vowel

Question 32

Could there be a situation in which each possible outcome has a different probability?

A)No, since every outcome must have exactly the same probability.
B)No, since outcome probabilities always have symmetric pairing.
C)No, since the Compton Limitation requires that at least one probability is shared by two outcomes.
D)Yes, as long as all of the probabilities add up to 1.
E)Yes, as long as the outcomes do not share any causal factors.

Question 33

Suppose that we use two different methods to determine the probability of a certain event.Will the two methods yield the same probability?

A)Yes, since the probability is always an objective fact.
B)Sometimes they will yield the same probability, and sometimes they won't.
C)They will yield the same result if they are used by the same person, but might not if they are used by two different people.
D)If one of the methods is intuitive judgment, then they will always be the same, but otherwise they might differ.
E)No, they can never yield the same results because their techniques are so different.

Question 34

Which of the following probabilities would be best determined by using the method of equal alternatives?

A)the odds that a randomly chosen person's favorite color will be blue
B)the odds that a randomly chosen food will contain butter
C)the odds that a randomly chosen vehicle will have four doors
D)the odds that a randomly chosen country will be in South America
E)the odds that a randomly chosen octopus will have all eight tentacles intact

Question 35

Which method for establishing probability would be most appropriate for determining the probability that the next man who walks into a certain restaurant will have a moustache?

A)method of equal alternatives
B)method of frequency
C)intuitive judgment
D)The methods would all be equally appropriate.
E)None of the methods could be applied in this situation.

Question 36

Which of the following probabilities would be best determined by using the method of frequency?

A)the odds that the next girl to enter a classroom will have red hair
B)the odds that there is life on one of Jupiter's moons
C)the odds that Morgan Freeman will play Batman in a movie
D)the odds that a certain senator will be reelected
E)the odds that a card selected randomly from a deck will be a four

Question 37

Which method for establishing probability requires the selection of a reference group?

A)method of frequency
B)guesstimation
C)method of equal alternatives
D)intuitive judgment
E)method of reference

Question 38

We can only apply the method of equal alternatives when the alternate outcomes are:

A)all events
B)all non-events
C)all favorable
D)equally likely to occur
E)equally important

Question 39

When the method of equal alternatives cannot be used to establish the probability of an event, one alternative is called:

A)the counting method
B)the Beard-Wasabi method
C)the method of quick assertion
D)the method of frequency
E)nothing at all; the method of equal alternatives is the only method

Question 40

One way to establish probability of an event, A, is to count the number of possible outcomes, n.Then divide the number of outcomes in which A occurs by n.This method is called the:

A)event probability generator
B)random chance calculator
C)count and divide technique
D)division method
E)method of equal alternatives

Question 41

Which method of establishing probability is most open to bias?

A)They are all equally open to bias.
B)intuitive judgment
C)method of frequency
D)method of equal alternatives
E)None of them is open to bias.

Question 42

Are probabilities based on intuitive judgments arbitrary and indifferent to evidence?

A)There are no probabilities based on intuitive judgments.
B)They are completely arbitrary, but they do take evidence into account.
C)They are not arbitrary, but they are completely indifferent to evidence.
D)Yes.
E)No.

Question 43

If event B is dependent on event A, then the probability that B will happen if A has happened is called _____ probability.

A)conditional
B)covalent
C)dependent
D)reciprocal
E)reflexive

Question 44

What is the probability of rolling two six-sided dice and getting two 5s?

A)1/5
B)1/6
C)1/36
D)1/18
E)1/30

Question 45

Which of the following probabilities would most likely be established by intuitive judgment?

A)the odds of winning the Publishers Clearing House Sweepstakes
B)the odds of actress Kristen Stewart becoming a museum curator
C)the odds of a fire starting in your home during the next month
D)the odds of a new radio station being profitable within a year
E)the odds of finding love on an Internet dating site

Question 46

Which of the following probabilities would most likely be established by intuitive judgment?

A)the odds that the Baltimore Ravens will win the Super Bowl
B)the odds that a vaccine will successfully prevent a disease
C)the odds that my pregnant friend's baby is a girl
D)the odds that a small business started in Chicago will be successful
E)the odds that a communications major will find employment within a year of graduation

Question 47

What is the probability of drawing a jack from a deck of cards, and then drawing a second jack from that same deck of cards?

A)1/13
B)1/26
C)1/52
D)1/221
E)7/2652

Question 48

Which of the following probabilities would most likely be established by intuitive judgment?

A)the odds that a circulating dollar is more than three years old
B)the odds that a certain dog will live to be 15 years old
C)the odds that lightning will strike my house this week
D)the odds that cars will get 90 miles to the gallon by the year 2050
E)the odds that a randomly chosen person voted in the last election

Question 49

Which operation of probability calculus would be used to determine the probability that there will not be a volcanic eruption in Italy during the next century?

A)conjunction
B)distribution
C)disjunction
D)negation
E)No operation of probability calculus could determine such a thing.

Question 50

Which operation of probability calculus would be used to determine the probability that there will be a storm tomorrow or your car will break down tomorrow?

A)conjunction
B)distribution
C)disjunction
D)negation
E)No operation of probability calculus could determine such a thing.

Question 51

The notation p(B\A) expresses the probability that:

A)B will happen before A
B)A will happen before B
C)B will cause A
D)either A or B will happen
E)B will happen, given that A has happened

Question 52

Which is the most complete and accurate list of the operations of probability calculus?

A)conjunction, negation
B)conjunction, distribution, disjunction, negation
C)conjunction, disjunction, negation
D)distribution, disjunction, negation
E)conjunction, disjunction

Question 53

What is the probability of rolling a six-sided die and getting a 2 on the first roll and a 4 on the second roll?

A)1/5
B)1/6
C)1/36
D)1/18
E)1/30

Question 54

A chess set has 16 white pieces and 16 black pieces.Half of the pieces of each color are pawns.Suppose that you are blindly removing chess pieces from a bag.What is the probability that the first two pieces you remove will be a white pawn and a black pawn (in either order)?

A)1/2
B)4/31
C)15/62
D)47/62
E)1/256

Question 55

In probability calculus, a conjunction is the probability that:

A)an event will not occur
B)one event will cause another
C)the same event will occur twice
D)two events will both occur
E)one or the other of two events will occur

Question 56

Which operation of probability calculus would be used to determine the probability that there will not be a fire drill at your job next week?

A)conjunction
B)distribution
C)disjunction
D)negation
E)No operation of probability calculus could determine such a thing.

Question 57

Which operation of probability calculus would be used to determine the probability that two different predictions made by a psychic, each with a known probability, will both come true?

A)conjunction
B)distribution
C)disjunction
D)negation
E)No operation of probability calculus could determine such a thing.

Question 58

The purpose of probability calculus is to:

A)determine simpler event probabilities
B)determine more complex event probabilities
C)eliminate the need for the method of frequency
D)eliminate the need for intuitive judgments
E)eliminate the need for the method of equal alternatives

Question 59

Which of the following probabilities would most likely be established by intuitive judgment?

A)the odds of being accepted into an Ivy League college
B)the odds of being audited by the IRS in a certain year
C)the odds of the paint in your house containing lead
D)the odds of your computer being infected by a virus in the next year
E)the odds of two particular countries being at war within the next decade

Question 60

A chess set has 16 white pieces and 16 black pieces.Suppose that you are blindly removing chess pieces from a bag.What is the probability that the first three pieces you remove will all be black?

A)1/45
B)45/256
C)3/32
D)3/31
E)7/62

Question 61

The probability that independent events A and B will both occur is determined by:

A)subtracting the probability of A from the probability of B
B)subtracting the probability of B from the probability of A
C)adding the probability of A to the probability of B
D)multiplying the probability of A by the probability of B
E)dividing the probability of A by the probability of B

Question 62

If I draw one card from a 52-card deck, what are the chances that it will not be a 7?

A)12/13
B)1/13
C)1/7
D)24/6,497,400
E)5,308,416/6,497,400

Question 63

If events A and B are compatible, how do we calculate the probability of their disjunction?

A)Subtract the probability of A from the probability of B.
B)Add the probability of A to the probability of B.
C)Add the probability of A to the probability of B and then subtract the probability of A and B both occurring.
D)Multiply the probability of A by the probability of B.
E)Divide the probability of A by the probability of B.

Question 64

How would we determine the probability of the negation of event A?

A)It is the same as the probability of event A.
B)It is the square of the probability of event A.
C)It is the square root of the probability of event A.
D)It is one minus the probability of event A.
E)It is the probability of event A minus one.

Question 65

What is the difference between mutually exclusive events and compatible events?

A)Two mutually exclusive events cannot both occur, whereas two compatible events can.
B)Two compatible events cannot both occur, whereas two mutually exclusive events can.
C)Two compatible events must both occur, whereas two mutually exclusive events might or might not both occur.
D)Two mutually exclusive events must both occur, whereas two compatible events might or might not both occur.
E)Mutually exclusive events are a category used for conjunction, whereas compatible events are a category used for disjunction.

Question 66

If events A and B are mutually exclusive, how do we calculate the probability of their disjunction?

A)Subtract the probability of A from the probability of B.
B)Add the probability of A to the probability of B.
C)Add the probability of A to the probability of B and then subtract the probability of A and B both occurring.
D)Multiply the probability of A by the probability of B.
E)Divide the probability of A by the probability of B.

Question 67

Is it possible to find the probability of the disjunction of more than two events?

A)Yes, but only if the events are compatible.
B)Yes, but only if the events are mutually exclusive.
C)Yes, for any number of events.
D)No, since the third event will always be mutually exclusive with one of the first two.
E)No, since the third event might be completely irrelevant to the first two.

Question 68

If a coin is flipped three times, what is the probability that all three flips will be heads or that all three flips will be tails?

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

Question 69

Suppose that the probability of one event is known from the method of equal alternatives, and the probability of a second event is known from intuitive judgment.Can the probability of both events occurring be determined through the operation of conjunction?

A)No, because no operation in probability calculus can be used with events that have probabilities which were established by different methods.
B)No, because conjunction cannot be used with events that have probabilities which were established by different methods.
C)No, because probabilities established by the method of equal alternatives are far more precise than those established by intuitive judgment.
D)Yes, but the resulting probability would be wildly inaccurate.
E)Yes, because the method by which probabilities were established has nothing to do with whether or not they can be conjoined.

Question 70

A chess set has 16 white pieces and 16 black pieces.Suppose that you are blindly removing chess pieces from a bag.What is the probability that the first two pieces you remove will both be black or both be white?

A)15/62
B)1/2
C)2/3
D)1/4
E)15/31

Question 71

Suppose that I flip a coin four times and it lands on heads all four times.How does this affect the probability that the next flip will also be heads?

A)It increases the probability by a factor of 4.
B)It increases the probability by a factor of 16.
C)It does not affect the probability at all.
D)It decreases the probability by a factor of 4.
E)It decreases the probability by a factor of 16.

Question 72

If I draw two cards from a 52-card deck, what is the probability that I will not draw two spades?

A)1/17
B)15/16
C)16/17
D)101/104
E)103/104

Question 73

If you are dealt two cards from a deck, what are the chances that they will both be red, or that they will both be aces?

A)29/1326
B)83/1326
C)331/1326
D)25/102
E)1/221

Question 74

In probability calculus, a disjunction is the probability that:

A)an event will not occur
B)one event will cause another
C)the same event will occur twice
D)two events will both occur
E)one or the other of two events will occur

Question 75

What is the difference between dependent and independent events?

A)The probability of an independent event depends on whether or not another event has occurred, whereas the probability of a dependent event does not.
B)The probability of a dependent event depends on whether or not another event has occurred, whereas the probability of an independent event does not.
C)Dependent events must both occur, whereas one independent event might occur without the other.
D)Independent events must both occur, whereas one dependent event might occur without the other.
E)Dependent events have a probability less than one half, whereas independent events have a probability that is one half or greater.

Question 76

A chess set has 16 white pieces and 16 black pieces.Half of the pieces of each color are pawns.Suppose that you are blindly removing chess pieces from a bag.What is the probability that the first two pieces you remove will be two black pawns or two white pawns?

A)7/62
B)7/124
C)1/16
D)1/8
E)3/32

Question 77

If there is a 20% chance of rain on the beach tomorrow, and a 0.003% chance of a shark attack, what is the probability that both events will happen?

A)0.0006%
B)20.003%
C)19.997%
D)0.06%
E)79.997%

Question 78

If there is a 10% chance that our exchange student will be from Asia, and a 20% chance that our exchange student will be from South America, what is the probability that the exchange student will be from Asia or South America?

A)30%
B)2%
C)10%
D)12%
E)28%

Question 79

If I draw one card from a deck, what are the chances that it will be a king, a queen, or a jack?

A)3/52
B)3/13
C)4/13
D)1/572
E)1/3

Question 80

In probability calculus, a negation is the probability that:

A)an event will not occur
B)one event will cause another
C)the same event will occur twice
D)two events will both occur
E)one or the other of two events will occur