PRINTABLE VERSION - UHcathy/Math2311/Lectures/may16.pdfThe probability that a randomly selected person has high blood pressure (the event H) is P(H) = 0.4 and the probability that

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PRINTABLE VERSIONQuiz 2

Question 1

A researcher randomly selects 4 fish from among 8 fish in a tank and puts each of the 4 selected fish intodifferent containers. How many ways can this be done?

a) 420

b) 128

c) 8400

d) 1680

e) 6720

f) None of the above

Question 2

An experimenter is randomly sampling 5 objects in order from among 49 objects. What is the total numberof samples in the sample space?

a) 1144130400

b) 1906884

c) 1086008

d) 228826080

e) 130320960


Question 3

A person eating at a cafeteria must choose 3 of the 17 vegetables on offer. Calculate the number of elementsin the sample space for this experiment.

a) 2040

b) 4080

c) 364



d) 680

e) 2184


Question 4

How many license plates can be made using 3 digits and 4 letters if repeated digits and letters are allowed?

a) 258336000

b) 775008000

c) 217002240000

d) 456976000

e) 1370928000


Question 5

The union of two events A and B is the event that:

a) Both A and B occur.

b) Either A or B or both occur.

c) A and B occur at the same time.

d) The intersection of A and B does not occur.

e) Either A or B, but not both occur.


Question 6

Let A = {3, 8}, B = {8, 12, 22}, D = {34} and S = sample space = A ∪ B ∪ D. Identify Ac.

a) {3, 12, 22, 34}

b) {3}

c) {34}

d) {12, 22, 34}



e) {12, 22}

f) None of the above.

Question 7

Let A = {2, 7}, B = {7, 20, 30}, D = {32} and S = sample space = A ∪ B ∪ D. Identify Bc ∪ A.

a) {2, 32}

b) {2, 20, 30, 32}

c) {2, 7, 20, 30}

d) {2, 7}

e) {2, 7, 32}


Question 8

Let A = {3, 10}, B = {10, 11, 28}, D = {35} and S = sample space = A ∪ B ∪ D. Identify (Ac ∩ Bc)c.

a) {11}

b) {3, 10, 11, 28}

c) {3}

d) {10}

e) {3, 10}


Question 9

Let A = {2, 7}, B = {7, 16, 22}, D = {34} and S = sample space = A ∪ B ∪ D. Identify Ac ∩ B.

a) {7}

b) {2, 16, 22}

c) {16, 22}

d) {7, 34}

e) {7, 16, 22}




Question 10

In a shipment of 71 vials, only 13 do not have hairline cracks. If you randomly select one vial from theshipment, what is the probability that it has a hairline crack?

a) 1⁄71

b) 13⁄58

c) 58⁄71

d) 13⁄71

e) 1⁄13


Question 11

Suppose a card is drawn from a deck of 52 playing cards. What is the probability of drawing a 6 or a queen?

a) 2⁄13

b) 1⁄13

c) 1⁄4

d) 1⁄156

e) 1⁄26


Question 12

The probability that a randomly selected person has high blood pressure (the event H) is P(H) = 0.4 and theprobability that a randomly selected person is a runner (the event R) is P(R) = 0.3. The probability that arandomly selected person has high blood pressure and is a runner is 0.2. Find the probability that a randomlyselected person either has high blood pressure or is a runner or both.

a) 0.8

b) 0.3

c) 0.7



d) 0.5

e) 0.6


Question 13

In a shipment of 58 vials, only 16 do not have hairline cracks. If you randomly select 2 vials from theshipment, what is the probability that none of the 2 vials have hairline cracks?

a) 0.5517

b) 0.4483

c) 0.0761

d) 0.0726

e) 0.9274


Question 14

The probability that a randomly selected person has high blood pressure (the event H) is P(H) = 0.4 and theprobability that a randomly selected person is a runner (the event R) is P(R) = 0.3. The probability that arandomly selected person has high blood pressure and is a runner is 0.2. Find the probability that a randomlyselected person has high blood pressure and is not a runner.

a) 0.5

b) 0.2

c) 0.7

d) 0.6

e) 0.4


Question 15

The probability that a randomly selected person has high blood pressure (the event H) is P(H) = 0.3 and theprobability that a randomly selected person is a runner (the event R) is P(R) = 0.4. The probability that arandomly selected person has high blood pressure and is a runner is 0.2. Select the false statement.

a) P(H ∩ Rc) = 0.1



b) P(Rc ∪ Hc) = 0.8

c) H and R are not mutually exclusive.

d) H and R are independent events.

e) P(R ∪ H) = 0.5


Question 16

Hospital records show that 12% of all patients are admitted for heart disease, 26% are admitted for cancer(oncology) treatment, and 4% receive both coronary and oncology care. What is the probability that arandomly selected patient is admitted for coronary care, oncology or both? (Note that heart disease is acoronary care issue.)

a) 0.34

b) 0.42

c) 0.62

d) 0.30

e) 0.38


Question 17

Hospital records show that 12% of all patients are admitted for heart disease, 26% are admitted for cancer(oncology) treatment, and 4% receive both coronary and oncology care. What is the probability that arandomly selected patient is admitted for something other than coronary care? (Note that heart disease is acoronary care issue.)

a) 0.70

b) 0.74

c) 0.84

d) 0.88

e) 0.96


Question 18



Among 7 electrical components exactly one is known not to function properly. If 2 components are randomlyselected, find the probability that all selected components function properly.

a) 0.2857

b) 0.6297

c) 0.5714

d) 0.8571

e) 0.7143


Question 19

Among 9 electrical components exactly one is known not to function properly. If 2 components are selectedrandomly, find the probability that exactly one does not function properly.

a) 0.2222

b) 0.8889

c) 0.1111

d) 0.7778

e) 0.7023


Question 20

Among 6 electrical components exactly one is known not to function properly. If 4 components are randomlyselected, find the probability that at least one does not function properly.

a) 0.6667

b) 0.5000

c) 0.5787

d) 0.8333

e) 0.3333




PRINTABLE VERSIONQuiz 3

Question 1

The probability that a randomly selected person has high blood pressure (the event H) is P(H) = 0.3 and theprobability that a randomly selected person is a runner (the event R) is P(R) = 0.5. The probability that arandomly selected person has high blood pressure and is a runner is 0.2. Find the probability that a randomlyselected person has high blood pressure, given that he is a runner.

a) 0.25

b) 0

c) 0.40

d) 1

e) 0.67


Question 2

The probability that a randomly selected person has high blood pressure (the event H) is P(H) = 0.4 and theprobability that a randomly selected person is a runner (the event R) is P(R) = 0.2. The probability that arandomly selected person has high blood pressure and is a runner is 0.1. Find the probability that a randomlyselected person is a runner, given that he has high blood pressure.

a) 0.25

b) 1

c) 0.50

d) 0.17

e) 0


Question 3

The probability that a student correctly answers on the first try (the event A) is P(A) = 0.1. If the studentanswers incorrectly on the first try, the student is allowed a second try to correctly answer the question (theevent B). The probability that the student answers correctly on the second try given that he answeredincorrectly on the first try is 0.2. Find the probability that the student correctly answers the question on thefirst or second try.



a) 0.30

b) 0.02

c) 0.26

d) 0.19

e) 0.28


Question 4

Given the following sampling distribution:

X -18 -13 -2 10 19

P(X) 1⁄259⁄100

7⁄1002⁄25 ___

What is P(X = 19)?

a) 0.74

b) 0.73

c) 0.72

d) 0.71

e) 0.19


Question 5


X -16 -11 -3 11 16

P(X) 1⁄203⁄100

1⁄209⁄100 ___

What is P(X > -11)?

a) 0.95

b) 0.92

c) 0.94



d) 0.90

e) 0.91


Question 6


X -16 -13 -7 11 14

P(X) 2⁄251⁄25

2⁄257⁄100 ___

What is the mean of this sampling distribution?

a) -2.2

b) 8.7

c) 8.4

d) -0.6

e) 8.6


Question 7

Suppose you have a distribution, X, with mean = 22 and standard deviation = 5. Define a new randomvariable Y = 8X - 3. Find the mean and standard deviation of Y.

a) E[Y] = 173; σY = 320

b) E[Y] = 176; σY = 37

c) E[Y] = 176; σY = 320

d) E[Y] = 173; σY = 40

e) E[Y] = 173; σY = 37


Question 8

In testing a certain kind of missile, target accuracy is measured by the average distance X (from the target) atwhich the missile explodes. The distance X is measured in miles and the sampling distribution of X is given



by:

X 0 10 50 100

P(X) 1⁄401⁄20

1⁄1033⁄40

Calculate the mean of this sampling distribution.

a) 27.6

b) 86.5

c) 88.0

d) 90.5

e) 761.0


Question 9

In testing a certain kind of missile, target accuracy is measured by the average distance X (from the target) atwhich the missile explodes. The distance X is measured in miles and the sampling distribution of X is givenby:

X 0 10 50 100

P(X) 1⁄121⁄6 1⁄3 5⁄12

Calculate the variance of this sampling distribution.

a) 2600.0

b) 60.0

c) 472.2

d) 1416.7

e) 37.6


Question 10

Suppose you want to play a carnival game that costs 5 dollars each time you play. If you win, you get $100.The probability of winning is 3⁄100. What is the expected value of the amount the carnival stands to gain?

a) 2.00



b) 3.00

c) 2.20

d) 2.30

e) -2.00


Question 11

Suppose you want to play a carnival game that costs 6 dollars each time you play. If you win, you get $100.The probability of winning is 1⁄50. What is the expected value of the amount that you, the player, stand togain?

a) -2.00

b) -4.20

c) -3.70

d) -4.00

e) 4.00


Question 12

A random sample of 2 measurements is taken from the following population of values: 1, 2, 4, 5, 8. What isthe probability that the range of the sample is 7?

a) 0.1

b) 0.3

c) 0.2

d) 0.5

e) 0.4


Question 13

A furniture store is having a sale on sofas and you're going to buy one. The advertisers know that buyers getto the store and that 1 out of 11 buyers change to a more expensive sofa than the one in the sale



advertisement. Let X be the cost of the sofa. What is the average cost of a sofa if the advertised sofa is $200and the more expensive sofa is $375?

a) 359.09

b) 215.80

c) 215.91

d) 214.58

e) 287.50


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PRINTABLE VERSION - UHcathy/Math2311/Lectures/may16.pdfThe probability that a randomly selected person has high blood pressure (the event H) is P(H) = 0.4 and the probability that