Deck 2: Introduction to Probability

Question 1

If A and B are mutually exclusive events,then P(A | B)= 0.

Answer 1

True

Question 2

In the set of all past due accounts,let the event A mean the account is between 31 and 60 days past due and the event B mean the account is that of a new customer.The complement of A is

A)all new customers.
B)all accounts fewer than 31 or more than 60 days past due.
C)all accounts from new customers and all accounts that are from 31 to 60 days past due.
D)all new customers whose accounts are between 31 and 60 days past due.

Answer 2

B

Question 3

Two events that are independent cannot be mutually exclusive.

Answer 3

False

Question 4

Two events that are mutually exclusive cannot be independent.

Question 5

A posterior probability is a conditional probability.

Question 6

P(A|B)= 1 − P(B|A)for all events A and B.

Question 7

P(A|B)= P(B|A)for all events A and B.

Question 8

The intersection of A and A^c is the entire sample space.

Question 9

If 50 of 250 people contacted make a donation to the city symphony,then the relative frequency method assigns a probability of .2 to the outcome of making a donation.

Question 10

An automobile dealership is waiting to take delivery of nine new cars.Today,anywhere from zero to all nine cars might be delivered.It is appropriate to use the classical method to assign a probability of 1/10 to each of the possible numbers that could be delivered.

Question 11

Which of the following is not a valid representation of a probability?

A)35%
B)0
C)1.04
D)3/8

Question 12

P(A|B)= P(A^C|B)for all events A and B.

Question 13

A list of all possible outcomes of an experiment is called

A)the sample space.
B)the sample point.
C)the experimental outcome.
D)the likelihood set.

Question 14

In the set of all past due accounts,let the event A mean the account is between 31 and 60 days past due and the event B mean the account is that of a new customer.The intersection of A and B is

A)all new customers.
B)all accounts fewer than 31 or more than 60 days past due.
C)all accounts from new customers and all accounts that are from 31 to 60 days past due.
D)all new customers whose accounts are between 31 and 60 days past due.

Question 15

A joint probability can have a value greater than 1.

Question 16

When assigning subjective probabilities,use experience,intuition,and any available data.

Question 17

In the set of all past due accounts,let the event A mean the account is between 31 and 60 days past due and the event B mean the account is that of a new customer.The union of A and B is

A)all new customers.
B)all accounts fewer than 31 or more than 60 days past due.
C)all accounts from new customers and all accounts that are from 31 to 60 days past due.
D)all new customers whose accounts are between 31 and 60 days past due.

Question 18

P(A|B)+ P(A|B^C)= 1 for all events A and B.

Question 19

Which of the following is not a proper sample space when all undergraduates at a university are considered?

A)S = {in-state,out-of-state}
B)S = {freshmen,sophomores}
C)S = {age under 21,age 21 or over}
D)S = {a major within business,no business major}

Question 20

The probability of an event

A)is the sum of the probabilities of the sample points in the event.
B)is the product of the probabilities of the sample points in the event.
C)is the maximum of the probabilities of the sample points in the event.
D)is the minimum of the probabilities of the sample points in the event.

Question 21

The range of probability is

A)any value larger than zero
B)any value between minus infinity to plus infinity
C)zero to one
D)any value between -1 to 1

Question 22

When the results of experimentation or historical data are used to assign probability values,the method used to assign probabilities is referred to as the

A)relative frequency method
B)subjective method
C)classical method
D)posterior method

Question 23

The complement of P(A | B)is

A)P(A^C | B)
B)P(A | B^C)
C)P(B | A)
D)P(A I B)

Question 24

Before drawing any conclusions about the relationship between two variables shown in a crosstabulation,you should

A)investigate whether any hidden variables could affect the conclusions
B)construct a scatter diagram and find the trendline
C)develop a relative frequency distribution
D)construct an ogive for each of the variables

Question 25

Of the last 100 customers entering a computer shop,25 have purchased a computer.If the classical method for computing probability is used,the probability that the next customer will purchase a computer is

A)0.25
B)0.50
C)0.75
D)1.00

Question 26

An experiment consists of tossing 4 coins successively.The number of sample points in this experiment is

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

Question 27

If P(A|B)= .2 and P(B^c)= .6,then P(B|A)

A)is .8
B)is .12
C)is .33
D)cannot be determined.

Question 28

Any process that generates well-defined outcomes is

A)an event
B)an experiment
C)a sample point
D)None of the other answers is correct.

Question 29

A method of assigning probabilities based upon judgment is referred to as the

A)relative method
B)probability method
C)classical method
D)None of the alternatives is correct.

Question 30

The probability of at least one head in two flips of a coin is

A)0.33
B)0.50
C)0.75
D)1.00

Question 31

An element of the sample space is

A)an event
B)an estimator
C)a sample point
D)an outlier

Question 32

The probability of an intersection of two events is computed using the

A)addition law
B)subtraction law
C)multiplication law
D)division law

Question 33

If P(A|B)= .4,then

A)P(B|A)= .6
B)P(A)*P(B)= .4
C)P(A)/ P(B)= .4
D)None of the alternatives is correct.

Question 34

Three applications for admission to a local university are checked to determine whether each applicant is male or female.The number of sample points in this experiment is

A)2
B)4
C)6
D)8

Question 35

A method of assigning probabilities that assumes the experimental outcomes are equally likely is referred to as the

A)objective method
B)classical method
C)subjective method
D)experimental method

Question 36

Revised probabilities of events based on additional information are

A)joint probabilities
B)posterior probabilities
C)marginal probabilities
D)complementary probabilities

Question 37

Posterior probabilities are computed using

A)the classical method
B)Chebyshev's theorem
C)the empirical rule
D)Bayes' theorem

Question 38

Posterior probabilities are

A)simple probabilities
B)marginal probabilities
C)joint probabilities
D)conditional probabilities

Question 39

The union of events A and B is the event containing

A)all the sample points common to both A and B
B)all the sample points belonging to A or B
C)all the sample points belonging to A or B or both
D)all the sample points belonging to A or B,but not both

Question 40

When the conclusions based upon the aggregated crosstabulation can be completely reversed if we look at the unaggregated data,the occurrence is known as

A)reverse correlation
B)inferential statistics
C)Simpson's paradox
D)disaggregation

Question 41

An experiment consists of four outcomes with P(E₁)= 0.2,P(E₂)= 0.3,and P(E₃)= 0.4.The probability of outcome E₄ is

A)0.500
B)0.024
C)0.100
D)0.900

Question 42

A graphical device used for enumerating sample points in a multiple-step experiment is a

A)bar chart
B)pie chart
C)histogram
D)None of the other answers is correct.

Question 43

Describe four experiments and list the experimental outcomes associated with each one.​

Question 44

Explain the difference between mutually exclusive and independent events.Can a pair of events be both mutually exclusive and independent?​

Question 45

A(n)__________ is a graphical representation in which the sample space is represented by a rectangle and events are represented as circles.

A)frequency polygon
B)histogram
C)Venn diagram
D)tree diagram

Question 46

One of the basic requirements of probability is

A)for each experimental outcome E_i,we must have P(E_i)≥ 1
B)P(A)= P(A^c)− 1
C)if there are k experimental outcomes,then P(E₁)+ P(E₂)+ ...+ P(E_k)= 1
D)both P(A)= P(A^c)− 1 and if there are k experimental outcomes,then P(E₁)+ P(E₂)+ ...+ P(E_k)= 1

Question 47

Use a tree diagram,labeled with appropriate notation,to illustrate Bayes' theorem.​

Question 48

Events A and B are mutually exclusive.Which of the following statements is also true?​

A)​A and B are also independent
B)​P(A Y B)= P(A)P(B)
C)​P(A Y B)= P(A)+ P(B)
D)​P(A ∩ B)= P(A)+ P(B)

Question 49

If A and B are mutually exclusive events with P(A)= 0.3 and P(B)= 0.5,then P(A ∩ B)=

A)0.30
B)0.15
C)0.00
D)0.20

Question 50

Draw a Venn diagram and label appropriately to show events A,B,their complements,intersection,and union.
​

Question 51

Compare these two descriptions of probability: 1)a measure of the degree of uncertainty associated with an event,and 2)a measure of your degree of belief that an event will happen.
​

Question 52

A package of candy contains 12 brown,5 red,and 8 green candies.You grab three pieces from the package.Give the sample space of colors you could get.Order is not important.

Question 53

Which of the following statements is(are)always true?

A)-1 ≤ P(E_i)≤ 1
B)P(A)= 1 − P(A^c)
C)P(A)+ P(B)= 1
D)both P(A)= 1 − P(A^c)and P(A)+ P(B)= 1

Question 54

Discuss the problems inherent in using words such as "likely," "possibly," or "probably" to convey degree of belief.​