Question 1

An auditing firm has developed a set of criteria for determining whether a particular account (and its balance)is in error.Historically,at companies where the gross sales are under $25 million,they know that of balances that were in error,75 percent were regarded as unusual.Assume Company A shows a history of only 10 percent of the account balances being in error and it also shows that 25 percent of the account balances were unusual.If in an audit,a particular account appears unusual,what is the probability that it is in error for Company A.

Accepted Answer

The answer of An auditing firm has developed a set...

Question 2

Suppose that A₁,A₂,and B are events where A₁ and A₂ are mutually exclusive events and P(A₁)= .7 P(A₂)= .3 P(B│A₁)= .2 P(B│A₂)= .4 Find P(A₂│B) A)0.12 B)0.26 C)0.21 D)0.14 E)0.46

Accepted Answer

P(A₂│B) = P(A₂∩B)/P(B) = .12/.26 = .46

Question 3

In a major midwestern university,55 percent of all undergraduates are female,25 percent of all undergraduates belong to a Greek organization (fraternity or sorority),and 40 percent of all males belong to a Greek organization.What is the probability that one randomly selected undergraduate will be either a female or belong to a Greek organization?
A).55
B).73
C).80
D).07
E).87

Accepted Answer

The probability that one randomly selected undergraduate will be either a female or belong to a Greek organization is the sum of the probabilities of being female and belonging to a Greek organization. The probability of being female is 0.55, and the probability of belonging to a Greek organization is 0.25. Therefore, the probability of being either female or belonging to a Greek organization is 0.55 + 0.25 = 0.80.

Question 4

Suppose the probability that an individual has a particular medical condition is .10.Tests of an individual's DNA can determine whether they have this medical condition but with only an 85 percent accuracy rate (that is,if the condition is present,the probability that the DNA test will give a positive finding is .85).If the medical condition is not present,the probability of the DNA test saying the medical condition exists is 0.03.What is the probability that the medical condition is present if the DNA test comes back positive?

Accepted Answer

The answer of Suppose the probability that an individual has...

Question 5

Suppose that A₁,A₂,and B are events where A₁ and A₂ are mutually exclusive events and P(A₁)= .7 P(A₂)= .3 P(B│A₁)= .2 P(B│A₂)= .4 Find P(A₁│B). A)0.12 B)0.26 C)0.21 D)0.14 E)0.28

Accepted Answer

The answer of Suppose that A₁,A₂,and B are events where...

Question 6

A worldwide personal products manufacturer is working on a new hair care product.In the past,85 percent of new hair care products introduced by this company have become successful (15 percent have failed).Obviously the marketing research department plays a large role in the introduction of any new product.Historically,85 percent of the successful products have a favorable rating from marketing research studies and 20 percent of the unsuccessful products have favorable ratings.For the new hair care product,the marketing unit has issued a favorable rating.What is the probability that the new product will be successful?

Accepted Answer

The answer of A worldwide personal products manufacturer is working...

Question 7

A television program director has 14 shows available for Monday night but can choose only 5 shows.How many different possible combinations are there?

Accepted Answer

The answer of A television program director has 14 shows...

Question 8

At a college,70 percent of the students are women,and 50 percent of the students receive a grade of C.25 percent of the students are neither female nor C students.Construct a contingency table.
 $\begin{array} { l c c r } 
& \mathrm { C } & \overline { \mathrm { C } } & \
\text { Women } & .45 & .25 & .70 \
\text { Men } & .05 & .25 & .30 \
& .50 & .50 & 1.00
\end{array}$

Accepted Answer

The answer of At a college,70 percent of the students...

Question 9

In a major midwestern university,55 percent of all undergraduates are female,25 percent of all undergraduates belong to a Greek organization (fraternity or sorority),and 40 percent of all males belong to a Greek organization.What percentage of the undergraduates are female and in a Greek organization?
A)55%
B)25%
C)60%
D)7%
E)15%

Accepted Answer

To complete the contingency table and answer the question on the intersection of female and Greek, since the initial information includes a conditional statement, you need to calculate the intersection of female and Greek: If P(Greek │ Male) = 40%. And 40% of .45 = .18. Then, Female & Greek = .25 − .18 = .07, or 7%
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Question 10

Suppose that A₁,A₂,and B are events where A₁ and A₂ are mutually exclusive events and P(A₁)= .7 P(A₂)= .3 P(B│A₁)= .2 P(B│A₂)= .4. Find P(B). A)0.60 B)0.26 C)0.21 D)0.14 E)0.28

Accepted Answer

P(B) = P(A₁) × P(B│A₁) + P(A₂) × P(B│A₂) = (.7)(.2) + (.3)(.4) = .26

Question 11

Suppose that you believe that the probability you will get a grade of B or better in Introduction to Finance is .6,and the probability that you will get a grade of B or better in Introduction to Accounting is .5.If these events are independent,what is the probability that you will receive a grade of B or better in both courses?
A)0.300
B)0.833
C)0.600
D)0.500
E)0.800

Accepted Answer

(.6)(.5) = .30

Question 12

An ad agency is developing a campaign to promote a business opening in a new mall development.To develop an appropriate mailing list,they decide to purchase lists of credit card holders from MasterCard and American Express.Combining the lists,they find the following: 40 percent of the people on the list have only a MasterCard and 10 percent have only an American Express card.Another 20 percent hold both MasterCard and American Express.Finally,30 percent of those on the list have neither card.Suppose a person on the list is known to have a MasterCard.What is the probability that person also has an American Express Card?
A).20
B).33
C).18
D).70
E).90

Accepted Answer

We want to find the probability that a person with a MasterCard also has an American Express card. 
Let's first find the total percentage of people on the list who have a MasterCard: 
40% have only a MasterCard + 20% have both MasterCard and American Express = 60%
So, out of 100 people on the list, 60 have a MasterCard.

Now, let's find the percentage of people with a MasterCard who also have an American Express: 
Out of the 60 people with a MasterCard, 20% (or 0.20) have both MasterCard and American Express. So, the probability that a person with a MasterCard also has an American Express is:

(20/100)/(60/100) = 20/60 = 1/3 = 0.33

Therefore, the answer is B) 33.

Question 13

Three companies produce all the potato chips used by vending machines in public areas in a midwestern state.Company A accounts for 70 percent of the chips,Company B 19 percent and Company C 11 percent.The probability of the vending company getting an unfilled bag is 2 percent for Company A,2 percent for Company B,and 4 percent for Company C.Suppose an unfilled bag is found.What is the probability that it came from Company A?

Accepted Answer

The answer of Three companies produce all the potato chips...

Question 14

Suppose that 60 percent of a company's computer chips are manufactured in Factory A,while 40 percent are produced in Factory B (P(A)= .60 for a randomly selected chip).The defect rates for the two factories are 35 percent for Factory A and 25 percent for Factory A..677 B.Suppose we now know that the randomly selected chip is defective.Find the probability that the defective chip comes from Factory A.

Accepted Answer

The answer of Suppose that 60 percent of a company's...

Question 15

An auditing firm has developed a set of criteria for determining whether a particular account (and its balance)is in error.Historically,at companies where the gross sales are under $25 million,they know that of balances that were in error,75 percent were regarded as unusual.Assume Company A shows a history of only 10 percent of the account balances being in error and it also shows that 25 percent of the account balances were unusual.What are the states of nature and the experimental outcomes?

Accepted Answer

The answer of An auditing firm has developed a set...

Question 16

In a major midwestern university,55 percent of all undergraduates are female,25 percent of all undergraduates belong to a Greek organization (fraternity or sorority),and 40 percent of all males belong to a Greek organization.What is the probability that an undergraduate is in a Greek organization,given that the undergraduate is a female?
A).07
B).55
C).127
D).039
E)138

Accepted Answer

To complete the contingency table and answer the question on the intersection of female or Greek, since the initial information includes a conditional statement, you need to calculate the intersection of male and Greek: If P(Greek │ Male) = 40%. And 40% of .45 = .18. Then, Female & Greek = .25 − .18 = .07, or 7%. P(Female) = 55%.
P(G|F) = .07/.55 = .127
 11ead627_0ab2_7e89_93a1_c5fb8750fc7f_TB7056_00

Question 17

Three companies produce all the potato chips used by vending machines in public areas in a midwestern state.Company A accounts for 70 percent of the chips,Company B 19 percent,and Company C 11 percent.The probability of the vending company getting an unfilled bag is 2 percent for Company A,2 percent for Company B,and 4 percent for Company C.Suppose an unfilled bag is found.What is the probability that it came from Company B?

Accepted Answer

The answer of Three companies produce all the potato chips...

Question 18

A batch of 50 parts contains 6 defects.If two parts are drawn randomly,one at a time,and tested,what is the probability that both parts are defective?
A)0.014
B)0.012
C)0.120
D)0.102
E)0.222

Accepted Answer

(6/50)(5/49) = .012

Question 19

In a major midwestern university,55 percent of all undergraduates are female,25 percent of all undergraduates belong to a Greek organization (fraternity or sorority),and 40 percent of all males belong to a Greek organization.Are the events "female/male" and "belongs to a Greek organization" independent?
A)Yes,independent
B)No,not independent
$\mathrm{P}(\mathrm{G} \mid \mathrm{F})=.07 / .55=.127 \neq \mathrm{P}(\mathrm{G})$

Accepted Answer

The events are not independent because the probability of belonging to a Greek organization is different for males and females. We can see this by calculating the conditional probabilities:

P(Greek organization | Female) = 0.07/0.55 = 0.127

P(Greek organization | Male) = 0.40

Since these probabilities are not equal, the events are not independent.

Question 20

In a local survey,100 citizens indicated their opinions on a revision to a local land-use plan.Of the 62 persons giving favorable responses,40 were males.Of the 38 giving unfavorable responses,15 were males.If one citizen is randomly selected,find the probability that person is has a favorable opinion or has an unfavorable opinion
A)0.00
B)1.00
C)0.62
D)0.24

Accepted Answer

The probability of selecting a person with either a favorable or unfavorable opinion is 1.00, as these are the only two possible opinions in the survey.

Quiz 4: Probability

Suppose that A₁,A₂,and B are events where A₁ and A₂ are mutually exclusive events and P(A₁) = .7 P(A₂) = .3 P(B│A₁) = .2 P(B│A₂) = .4 Find P(A₂│B)

Suppose that A₁,A₂,and B are events where A₁ and A₂ are mutually exclusive events and P(A₁) = .7 P(A₂) = .3 P(B│A₁) = .2 P(B│A₂) = .4 Find P(A₁│B) .

A television program director has 14 shows available for Monday night but can choose only 5 shows.How many different possible combinations are there?

Suppose that A₁,A₂,and B are events where A₁ and A₂ are mutually exclusive events and P(A₁) = .7 P(A₂) = .3 P(B│A₁) = .2 P(B│A₂) = .4. Find P(B) .

A batch of 50 parts contains 6 defects.If two parts are drawn randomly,one at a time,and tested,what is the probability that both parts are defective?

Quiz 4: Probability

Suppose that A1,A2,and B are events where A1 and A2 are mutually exclusive events and P(A1) = .7 P(A2) = .3 P(B│A1) = .2 P(B│A2) = .4 Find P(A2│B)

Suppose that A1,A2,and B are events where A1 and A2 are mutually exclusive events and P(A1) = .7 P(A2) = .3 P(B│A1) = .2 P(B│A2) = .4 Find P(A1│B) .

A television program director has 14 shows available for Monday night but can choose only 5 shows.How many different possible combinations are there?

Suppose that A1,A2,and B are events where A1 and A2 are mutually exclusive events and P(A1) = .7 P(A2) = .3 P(B│A1) = .2 P(B│A2) = .4. Find P(B) .

A batch of 50 parts contains 6 defects.If two parts are drawn randomly,one at a time,and tested,what is the probability that both parts are defective?

Suppose that A₁,A₂,and B are events where A₁ and A₂ are mutually exclusive events and P(A₁) = .7 P(A₂) = .3 P(B│A₁) = .2 P(B│A₂) = .4 Find P(A₂│B)

Suppose that A₁,A₂,and B are events where A₁ and A₂ are mutually exclusive events and P(A₁) = .7 P(A₂) = .3 P(B│A₁) = .2 P(B│A₂) = .4 Find P(A₁│B) .

Suppose that A₁,A₂,and B are events where A₁ and A₂ are mutually exclusive events and P(A₁) = .7 P(A₂) = .3 P(B│A₁) = .2 P(B│A₂) = .4. Find P(B) .