Deck 2: Introduction to Probability

Question 1

If P(A $\cap$ B)= 0

A)A and B are independent events.
B)P(A)+ P(B)= 1
C)A and B are mutually exclusive events.
D)either P(A)= 0 or P(B)= 0.

Answer 1

A and B are mutually exclusive events.

Question 2

A joint probability can have a value greater than 1.

Answer 2

False

Question 3

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

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

Answer 3

C

Question 4

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 5

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.

Question 6

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 7

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 8

Two events that are independent cannot be mutually exclusive.

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

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 12

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 13

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 14

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 15

If P(A)= 0.38,P(B)= 0.83,and P(A $\cap$ B)= 0.27;then P(A $\cup$ B)=

A)1.21
B)0.94
C)0.72
D)1.48

Question 16

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 17

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

Question 18

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 19

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 20

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 21

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

Question 22

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

Question 23

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

Question 24

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

Question 25

Two events that are mutually exclusive cannot be independent.

Question 26

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

Question 27

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

Question 28

If A and B are independent events,then P(A $\cap$ B)= P(A)P(B).

Question 29

An investment advisor recommends the purchase of shares in Probaballisitics,Inc.He has made the following predictions:
P(Stock goes up 20% | Rise in GDP)= .6
P(Stock goes up 20% | Level GDP)= .5
P(Stock goes up 20% | Fall in GDP)= .4
An economist has predicted that the probability of a rise in the GDP is 30%,whereas the probability of a fall in the GDP is 40%.
a.What is the probability that the stock will go up 20%?
b.We have been informed that the stock has gone up 20%.What is the probability of a rise or fall in the GDP?

Question 30

If P(A $\cup$ B)= P(A)+ P(B),then A and B are mutually exclusive.

Question 31

Global Airlines operates two types of jet planes: jumbo and ordinary.On jumbo jets,25% of the passengers are on business while on ordinary jets 30% of the passengers are on business.Of Global's air fleet,40% of its capacity is provided on jumbo jets.(Hint: The 25% and 30% values are conditional probabilities stated as percentages. )
a.What is the probability a randomly chosen business customer flying with Global is on a jumbo jet?
b.What is the probability a randomly chosen non-business customer flying with Global is on an ordinary jet?

Question 32

Bayes' theorem provides a way to transform prior probabilities into posterior probabilities.

Question 33

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

Question 34

If P(A|B)= .4 and P(B)= .6,then P(A $\cap$ B)= .667.

Question 35

P(A $\cap$ B) $\ge$ P(A)

Question 36

If A and B are independent events with P(A)= 0.1 and P(B)= 0.5,then P(A  B)= .6.

Question 37

A posterior probability is a conditional probability.

Question 38

An accounting firm has noticed that of the companies it audits,85% show no inventory shortages,10% show small inventory shortages and 5% show large inventory shortages.The firm has devised a new accounting test for which it believes the following probabilities hold:
P(company will pass test | no shortage)= .90
P(company will pass test | small shortage)= .50
P(company will pass test | large shortage)= .20
a.If a company being audited fails this test,what is the probability of a large or small inventory shortage?
b.If a company being audited passes this test,what is the probability of no inventory shortage?

Question 39

A market study taken at a local sporting goods store showed that of 20 people questioned,6 owned tents,10 owned sleeping bags,8 owned camping stoves,4 owned both tents and camping stoves,and 4 owned both sleeping bags and camping stoves.
Let: Event A = owns a tent
Event B = owns a sleeping bag
Event C = owns a camping stove
and let the sample space be the 20 people questioned.
a.Find P(A),P(B),P(C),P(ASYMBOL 199 \f "Symbol"C),P(BSYMBOL 199 \f "Symbol"C).
b.Are the events A and C mutually exclusive? Explain briefly.
c.Are the events B and C independent events? Explain briefly.
d.If a person questioned owns a tent,what is the probability he also owns a camping stove?
e.If two people questioned own a tent,a sleeping bag,and a camping stove,how many own only a camping stove? In this case is it possible for 3 people to own both a tent and a sleeping bag,but not a camping stove?

Question 40

The following probability model describes the number of snow storms for Washington,D.C.for a given year:
The probability of 7 or more snowstorms in a year is 0.
a.What is the probability of more than 2 but less than 5 snowstorms?
b.Given this a particularly cold year (in which 2 snowstorms have already been observed),what is the conditional probability that 4 or more snowstorms will be observed?
c.If at the beginning of winter there is a snowfall,what is the probability of at least one more snowstorm before winter is over?

Question 41

A medical research project examined the relationship between a subject's weight and recovery time from a surgical procedure,as shown in the table below.

a.Use relative frequency to develop a joint probability table to show the marginal probabilities.
b.What is the probability a patient will recover in fewer than 3 days?
c.Given that recovery takes over 7 days,what is the probability the patient is overweight?

Question 42

Super Cola sales breakdown as 80% regular soda and 20% diet soda.While 60% of the regular soda is purchased by men,only 30% of the diet soda is purchased by men.If a woman purchases Super Cola,what is the probability that it is a diet soda?

Question 43

To better track its patients,a hospital's neighborhood medical center has gathered this information.

a.Develop a joint probability table.Include the marginal probabilities.
b.Find the conditional probabilities:
P(A|N),P(A|E),P(W|N),P(W|E),P(N|A),P(E|A),P(N|W),P(E|W)

Question 44

It is estimated that 3% of the athletes competing in a large tournament are users of an illegal drug to enhance performance.The test for this drug is 90% accurate.What is the probability that an athlete who tests positive is actually a user?

Question 45

Safety Insurance Company has compiled the following statistics.For any one year period:
The percentage of Safety's policyholders in each category are:

a.What is the probability that a randomly selected policyholder will have an accident within the next year?
b.Given that a driver has an accident,what is the probability that the driver is a male over 25?
c.Given that a driver has no accident,what is the probability the driver is a female?
d.Does knowing the fact that a driver has had no accidents give us a great deal of information regarding the driver's sex?

Question 46

Mini Car Motors offers its luxury car in three colors: gold,silver and blue.The vice president of advertising is interested in the order of popularity of the color choices by customers during the first month of sales.
a.How many sample points are there in this experiment?
b.If the event A = gold is the most popular color,list the outcome(s)in event A.
c.If the event B = blue is the least popular color,list the outcome(s)in ASYMBOL 199 \f "Symbol"B.
d.List the outcome(s)in ASYMBOL 199 \f "Symbol"B^c.

Question 47

A mail order company tracks the number of returns it receives each day.Information for the last 50 days shows

a.How many sample points are there?
b.List and assign probabilities to sample points.
c.What procedure was used to assign these probabilities?

Question 48

Through a telephone survey,a low-interest bank credit card is offered to 400 households.The responses are as tabled.

a.Develop a joint probability table and show the marginal probabilities..
b.What is the probability of a household whose income exceeds $40,000 and who rejects the offer?
c.If income is < $40,000,what is the probability the offer will be accepted?
d.If the offer is accepted,what is the probability that income exceeds $40,000?

Question 49

A food distributor carries 64 varieties of salad dressing.Appleton Markets stocks 48 of these flavors.Beacon Stores carries 32 of them.The probability that a flavor will be carried by Appleton or Beacon is 15/16.Use a Venn diagram to find the probability a flavor is carried by both Appleton and Beacon.

Question 50

There are two more assignments in a class before its end,and if you get an A on at least one of them,you will get an A for the semester.Your subjective assessment of your performance is

a.What is the probability of getting an A on the paper?
b.What is the probability of getting an A on the exam?
c.What is the probability of getting an A in the course?
d.Are the grades on the assignments independent?

Question 51

The Ambell Company uses batteries from two different manufacturers.Historically,60% of the batteries are from manufacturer 1,and 90% of these batteries last for over 40 hours.Only 75% of the batteries from manufacturer 2 last for over 40 hours.A battery in a critical tool fails at 32 hours.What is the probability it was from manufacturer 2?

Question 52

Higbee Manufacturing Corp.has recently received 5 cases of a certain part from one of its suppliers.The defect rate for the parts is normally 5%,but the supplier has just notified Higbee that one of the cases shipped to them has been made on a misaligned machine that has a defect rate of 97%.So the plant manager selects a case at random and tests a part.
a.What is the probability that the part is defective?
b.Suppose the part is defective,what is the probability that this is from the case made on the misaligned machine?
c.After finding that the first part was defective,suppose a second part from the case is tested.However,this part is found to be good.Using the revised probabilities from part (b)compute the new probability of these parts being from the defective case.
d.Do you think you would obtain the same posterior probabilities as in part (c)if the first part was not found to be defective but the second part was?
e.Suppose,because of other evidence,the plant manager was 80% certain this case was the one made on the misaligned machine.How would your answer to part (b)change?

Question 53

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.