Question 1

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

P(AE|MC) = .20/.60 = .33
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Question 2

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 3

New car owners were asked to evaluate their experiences in buying a new car during the past 12 months.In the survey,the owners indicated they were most satisfied with their experiences at the following three dealers (in no particular order): Subaru,Honda,and Buick.When ranking the dealers,how many outcomes are possible?
A)6
B)9
C)8
D)10
E)12

Accepted Answer

HSB, BHS, SHB, HBS, BSH, SBH

Question 4

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 male and has a favorable opinion.
A)0.40
B)0.65
C)0.62
D)0.55
E)0.25

Accepted Answer

40/100

Question 5

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 6

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 7

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
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Question 8

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

Accepted Answer

Two events are independent if the occurrence of one event does not affect the probability of the other event. However, in this case, the occurrence of the event "belongs to a Greek organization" is not independent of the event "male/female". We know that 40 percent of all males belong to a Greek organization, but we do not know the percentage of females who belong to a Greek organization. Therefore, the events are not independent.

Question 9

New car owners were asked to evaluate their experiences in buying a new car during the past 12 months.In the survey,the owners indicated they were most satisfied with their experiences at the following three dealers (in no particular order): Subaru,Honda,and Buick.Assuming that each set of rankings is equally likely,what is the probability that owners ranked Subaru first?
A)1/3
B)1/6
C)1/2
D)5/6
E)6/6

Accepted Answer

Sample spaces: HSB, BHS, SHB, HBS, BSH, SBH; 2/6, or 1/3

Question 10

New car owners were asked to evaluate their experiences in buying a new car during the past 12 months.In the survey,the owners indicated they were most satisfied with their experiences at the following three dealers (in no particular order): Subaru,Honda,and Buick.Assuming that each set of rankings is equally likely,what is the probability that owners ranked Subaru first and Honda second?
A)1/3
B)1/6
C)1/2
D)5/6
E)6/6

Accepted Answer

Since there are three dealers, there are 3! = 6 possible orders in which the owners could rank the dealerships. Since each order is equally likely, the probability that an owner ranks Subaru first and Honda second is the probability that they rank the three dealerships in the order "Subaru, Honda, Buick" or "Buick, Subaru, Honda". Each of these orders has a probability 1/6, so the total probability is 1/6 + 1/6 = 1/3. Therefore, the answer is (B) 1/6.

Question 11

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 12

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 answer of In a local survey,100 citizens indicated their...

Question 13

New car owners were asked to evaluate their experiences in buying a new car during the past 12 months.In the survey,the owners indicated they were most satisfied with their experiences at the following three dealers (in no particular order): Subaru,Honda,and Buick.Assuming that each set of rankings is equally likely,what is the probability that owners ranked Subaru third?
A)1/3
B)1/6
C)1/2
D)5/6
E)6/6

Accepted Answer

Sample spaces: HSB, BHS, SHB, HBS, BSH, SBH; 2/6, or 1/3

Question 14

In a study of chain saw injuries,57 percent involved arms or hands.If three different chain saw injury cases are randomly selected,find the probability that they all involved arms or hands.
A)0.570
B)0.190
C)0.185
D)0.829
E)0.325

Accepted Answer

The probability of one randomly selected chain saw injury involving arms or hands is 0.57. Since we are selecting three different cases, we can use the multiplication rule of probability. 
P(all three involved arms or hands) = P(first case involves arms or hands) x P(second case involves arms or hands) x P(third case involves arms or hands) = 0.57 x 0.57 x 0.57 = 0.185. 
Therefore, the answer is choice C.

Question 15

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 answer of In a major midwestern university,55 percent of...

Question 16

A survey is made in a neighborhood of 80 voters.65 are Democrats and 15 are Republicans.Of the Democrats,35 are women,while 5 of the Republicans are women.If one subject from the group is randomly selected,find the probability the individual is a Democrat or a Republican.
A)0.50
B)1.00
C)0.813
D)0.188
E)0.152

Accepted Answer

All voters in the survey were either D or R. Therefore, the probability is 1.

Question 17

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 18

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 female or has an unfavorable opinion.
A)0.83
B)0.17
C)0.51
D)0.60
E)0.61

Accepted Answer

P(F ∪ N) = P(F) + P(N) - P(F ∩ N) = .45 + .38 - .23 = .60
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Question 19

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 20

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

Quiz 4: Probability

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(A₁|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?

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

A survey is made in a neighborhood of 80 voters.65 are Democrats and 15 are Republicans.Of the Democrats,35 are women,while 5 of the Republicans are women.If one subject from the group is randomly selected,find the probability the individual is a Democrat or a Republican.

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) .

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) .

Quiz 4: Probability

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(A1|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?

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

A survey is made in a neighborhood of 80 voters.65 are Democrats and 15 are Republicans.Of the Democrats,35 are women,while 5 of the Republicans are women.If one subject from the group is randomly selected,find the probability the individual is a Democrat or a Republican.

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) .

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) .

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) .