Finite Math (30 Question)

QUESTION 1

An experiment consists of tossing a coin, rolling a die, and observing the outcomes. Describe an appropriate sample space for this experiment.
a.{(1, H, T), (2, H, T), (3, H, T), (4, H, T), (5, H, T), (6, H, T)}

b.{( H, 1), ( T, 2), ( H, 3), ( T, 4), ( H, 5), ( T, 6), ( T, 1), ( T, 4), ( T, 5), ( H, 6)}

c.{( H, 1), ( H, 2), ( H, 3), ( H, 4), ( H, 5), ( H, 6), ( T, 1), ( T, 2), ( T, 3), ( T, 4), ( T, 5), ( T, 6)}

d.{(1, 2, 3, 4, 5, 6), ( H, T)}e.{( H, H, H, H, H, H, T, T, T, T, T, T, 1, 2, 3, 4, 5, 6)}

1 points  

QUESTION 2

A sample of two transistors taken from a local electronics store was examined to determine whether the transistors were defective ( d) or nondefective ( n). What is an appropriate sample space for this experiment?

​a.{ dd, nn, nd}

b.{ dd, dn, nd}

c.{ dd, dn, nd, nn}

d.{ (d,d), (n,n)}

1 points  

QUESTION 3

Eight players, A, B, C, D, E, F, G, and H, are competing in a series of elimination matches of a tennis tournament in which the winner of each preliminary match will advance to the semifinals and the winner of the semifinals will advance to the finals. An outline of the scheduled matches follows. Describe a sample space listing the possible participants in the finals.

a.S = {( A,D), ( A,F), ( A,H), ( C,B), ( C,F), ( C,H), ( E,B), ( E,D), ( E, H), ( G,B),(G,D), (G,F)}

b.S = {( A,B), ( A,D), ( A,F), ( A,H), ( C,B), ( C,D), ( C,F), ( C,H), ( E,B), ( E,D),(E,F), (E, H), (G,B), (G,D), (G,F), (G,H)}

c.S = {( A,E), ( A,F), ( A,G), ( A,H), ( B,E), ( B,F), ( B,G), ( B,H), ( C, E), ( C,F),(C,G), (C,H), (D,E), (D,F), (D,G), (D,H)}

d.S = {( A,B), ( A,C), ( A,D), ( B,С), ( B,D), ( C,D), ( E,F), ( E,G), ( E, H), ( F,G),(F,H), (G,H)}

e.None of the above.

1 points  

QUESTION 4

An experiment consists of selecting a card from a standard deck of playing cards and noting whether the card is black ( B) or red ( R). What are the events of this experiment?

​a.{ B}, { R}, { B, B}, { R, R}

b.{ B, R}, { R, B}

c.{Ø}, { B, R}, { R, B}, { R, R}, { B, B}

d.{Ø}, { B}, { R}

e.{Ø}, { B}, { R}, { B, R}

1 points  

QUESTION 5

Let  be a sample space of an experiment with outcomes p, q and  r. List all the events of this experiment.​

a.Ø, { p}, { q}, { r},  { p , q }, { p , r }, {q, r}, S

b.{ p }, { q }, { r },  { p ,  q },  { p ,  r }, {q, r}

c.Ø, { p }, { q }, { r },  { p ,  q },  { p ,  r }, {q, r}d.{ p }, { q }, { r}

1 points  

QUESTION 6

The customer service department of Universal Instruments, manufacturer of the Galaxy home computer, conducted a survey among customers who had returned their purchase registration cards. Purchasers of its deluxe model home computer were asked to report the length of time ( t) in days before service was required.

Describe a sample space corresponding to this survey.
a.{ t | 100 ≤ t ≤ 370}

b.{ t | 0 < t ≤ 370}

c.{ t | t > 0}d.{ t | 0 < t ≤ 100}

1 points  

QUESTION 7

Let  be a sample space of an experiment and let , and  be events of this experiment.​
Find the events E ∪ F and E ∩ F.
​a.

b.

c.

d.

1 points  

QUESTION 8

In a television game show, the winner is asked to select three prizes from five different prizes, A, B, C, D, and E.

Describing a sample space of possible outcomes (order is not important) determine the number of points there are in the sample space corresponding to a selection that includes A.
a.6

b.2

c.9

d.4

1 points  

QUESTION 9

Human blood is classified by the presence or absence of three main antigens (A, B, and Rh). When a blood specimen is typed, the presence of the A and/or B antigen is indicated by listing the letter A and/or the letter B. If neither the A nor B antigen is present, the letter O is used. The presence or absence of the Rh antigen is indicated by the symbols + or -, respectively. Thus, if a blood specimen is classified as AB +, it contains the A and the B antigens as well as the Rh antigen. Similarly, O- blood contains none of the three antigens.

Using this information, determine the sample space corresponding to the different blood groups.
a.{ AB+, AB-, AO+, BO+, AO-, BO-, O+, O-}

b.{ AB+, AB-, O+, O-}

c.{ AB+, AB-, A+, B+, A-, B-, O+, O-, ABO-, AO+, AO-, BO+, BO-}

d.{ AB+, AB-, A+, B+, A-, B-, O+, O-}e.{ A+, B+, A-, B-, O+, O-}

1 points  

QUESTION 10

An experiment consists of selecting a card from a standard deck of playing cards and noting whether the card is black ( B) or red ( R). Describe an appropriate sample space for this experiment.​a.{ R, R}

b.{ R, B, B, R}

c.{ B, B}

d.{ BR, RB}

e.{ B, R}

1 points  

QUESTION 11

Let  be a sample space of an experiment and let  be events of this experiment.​
Are the events E and F mutually exclusive?
​a.no

b.yes

1 points  

QUESTION 12

Let  be a sample space associated with an experiment.

How many subsets of S contain either the number 2 or the number 1?
a.5

b.7

c.3

d.6

e.4

1 points  

QUESTION 13

An experiment consists of casting a pair of dice and observing the number that falls uppermost on each die. We may represent each outcome of the experiment by an ordered pair of numbers, the first representing the number that appears uppermost on the first die and the second representing the number that appears uppermost on the second die. Consider the sample space

S = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),        (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6),
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}

Determine the event that the number that falls uppermost on the first die is greater than the number that falls uppermost on the second die.
a.{(2, 1), (3, 1), (4, 1), (5, 1), (6, 1), (3, 2), (4, 2), (5, 2), (6, 2), (4, 3), (5, 3), (6, 3), (5, 4), (6, 4), (6, 5)}

b.{(1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (3, 2), (4, 2), (5, 2), (6, 2), (4, 3), (5, 3), (6, 3), (5, 4), (6, 4), (5, 6)}

c.{(2, 1), (3, 1), (4, 1), (5, 1), (6, 1), (2, 3), (2, 4), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6), (4, 5), (6, 4), (6, 5)}

d.Ø

1 points  

QUESTION 14

Let S = {1, 2, 3, 4, 5, 6}, E = {1, 3, 5}, F = {2, 4, 6} and G = {2, 3}.

Are the events F and G mutually exclusive?
a.yes

b.no

1 points  

QUESTION 15

A die is cast and the number that falls uppermost is observed. Let E denote the event that the number shown is a 6 and let F denote the event that the number shown is an even number.​
Are the events E and F mutually exclusive?
​a.yes

b.no

Two

QUESTION 1

The grade distribution for a certain class is shown in the table. Find the probability distribution associated with these data.
GradeABCDFFrequency of Occurrence481864

​

a.GradeABCDFFrequency of0.110.2 0.430.15 0.11Occurrence

​b.​GradeABCDFFrequency of0.1 0.21 0.430.160.1 Occurrence

​c.​GradeABCDFFrequency of0.10.15 0.450.2 0.1Occurrence     ​

d.GradeABCDFFrequency of0.1 0.2 0.45 0.15 0.1Occurrence     ​

1 points  

QUESTION 2

The grade distribution for a certain class is shown in the table.
GradeABCDFFrequency of Occurrence462262What is the probability that a student selected at random from this class received a passing grade (D or better)?

 a.The probability is 0.95

b.The probability is 0.93

c.The probability is 0.99

d.The probability is 0.97

1 points  

QUESTION 3

If a ball is selected at random from an urn containing two red balls, three white balls, and five blue balls, what is the probability that it will be a white ball?

a.The probability is 0.32

b.The probability is 0.33

c.The probability is 0.30

d.The probability is 0.31

1 points  

QUESTION 4

According to a survey of 176 retailers, 41% of them use electronic tags as protection against shoplifting and employee theft. If one of these retailers is selected at random, what is the probability that he or she uses electronic tags as anti-theft devices?

a.The probability is 0.43

b.The probability is 0.42

c.The probability is 0.41

d.The probability is 0.40

1 points  

QUESTION 5

What is the probability of arriving at a traffic light when it is red if the red signal is flashed for 35 sec, the yellow signal for 5 sec, and the green signal for 60 sec?

a.The probability is 0.40

b.The probability is 0.45

c.The probability is 0.30

d.The probability is 0.35

1 points  

QUESTION 6

Consider the composition of a three-child family in which the children were born at different times. Assume that a girl is as likely as a boy at each birth.

What is the probability that there are two girls and a boy in the family?
a.

b.

c.

d.

e.

1 points  

QUESTION 7

The percentage of the general population that has each blood type is shown in the table:
Blood TypeABABOPopulation, %4011346
Determine the probability distribution associated with these data.

a.Blood Type       A       B       AB      O 
Population, %   0.42    0.13    0.03    0.42

b.Blood Type       A       B       AB      O 
Population, %   0.36    0.11    0.05    0.48

c.Blood Type       A       B       AB      O 
Population, %   0.46    0.03    0.11    0.4

d.Blood Type       A       B       AB      O 
Population, %   0.4     0.11    0.03    0.46

1 points  

QUESTION 8

Determine whether the given experiment has a sample space with equally likely outcomes.

Two fair dice are cast, and the sum of the numbers appearing uppermost is recorded.

a.no

b.yes

1 points  

QUESTION 9

The following breakdown of a total of 18,613 transportation fatalities that occured in 2007 was obtained from records compiled by the U.S. Department of Transportation (DOT).
Mode of TransportationCarTrainBicyclePlaneNumber of Fatalities16,525850698540What is the probability that a victim randomly selected from this list of transportation fatalities for 2007 died in a car crash or bicycle accident? Round answer to two decimal places.
a.0.98

b.0.93

c.0.92

d.0.89

1 points  

QUESTION 10

In a survey of 3000 adults 18 year old and older conducted in 2000, the following question was asked : Is your family income keeping pace with the cost of living ? The results of the survey follow :
AnswerFalling behindStaying evenIncreasing fasterDon’t knowRespondents12001040560200Determine the empirical probability distribution associated with these data.

a.​AnswerFalling
behindStaying
evenIncreasing
fasterDon’t
knowNumber of
Respondents:0.300.450.240.12

b.​AnswerFalling
behindStaying
evenIncreasing
fasterDon’t
knowNumber of
Respondents:0.400.300.140.17

​c.​AnswerFalling
behindStaying
evenIncreasing
fasterDon’t
knowNumber of
Respondents:0.300.250.250.32

​d.​AnswerFalling
behindStaying
evenIncreasing
fasterDon’t
knowNumber of
Respondents:0.400.350.190.07​
​

1 points  

QUESTION 11

One light bulb is selected at random from a lot of 140 light bulbs, of which 2% are defective. What is the probability that the light bulb selected is defective?​

a.The probability is 0.04

b.The probability is 0.01

c.The probability is 0.03

d.The probability is 0.02

1 points  

QUESTION 12

In a survey of 700 likely voters, the following question was asked: Do you support using cameras to identify red-light runners? The results of the survey follow:
AnswerStrongly supportSomewhat
supportSomewhat
opposeStrongly
OpposeDon’t
knowRespondents3201758011510

What is the probability that a person in the survey selected at random favors using cameras to identify red-light runners?
a.0.61

b.0.71

c.0.66

d.0.29

1 points  

QUESTION 13

The number of subscribers to five leading e-mail services is shown in the accompanying table:
CompanyABCDESubscribers370,000150,000110,000100,00070,000Find the empirical probability distribution associated with these data.
a.​Company A B C D E Subscribers 0.4625   0.1875   0.1367   0.1254   0.0879   ​
​b.​Company ​A ​B C D E Subscribers 0.4625   0.1875   0.1375   0.125   0.0875   ​
​c.​Company A B C D E Subscribers 0.0875   0.125   0.1375   0.1875   0.4625 ​
​d.​Company A B C D E Subscribers 0.4609   0.1879   0.1379   0.1254   0.0879   ​
​

1 points  

QUESTION 14

According to Mediamark Research, 86 million out of 179 million adults in the United States correct their vision by using prescription eyeglasses, bifocals, or contact lenses. (Some respondents use more than one type.) What is the probability that an adult selected at random from the adult population uses corrective lenses? Round your answer to the nearest thousandth.

a.The probability is 0.480

b.The probability is 0.479

c.The probability is 0.481

d.The probability is 0.001

1 points  

QUESTION 15

Let  be the sample space associated with an experiment having the following probability distribution:
Outcomes1s2s3s4s5s6Probability
Find the probability of the event .
a.The probability is 

b.The probability is 

c.The probability is 

d.The probability is 0